Index to continued fractions for sqrt(n)

Introduction

Euler and Lagrange showed that continued fractions for quadratic irrational numbers are eventually periodic, and vice versa. The OEIS contains over 3500 entries for sequences related to the continued fractions for sqrt(n). See also the main Index to OEIS and the wiki page for continued fractions. In the following lists use three variables:

• n is the index for the sequence terms a(n),
• k is a number for which the continued fraction of sqrt(k) fulfills some condition,
• m is a parameter for that condition.

Example

The following table shows [floor(sqrt(n));period] of the continued fractions for sqrt(n), n = 25..36. There is a table up 20000.

25 [5]
26 [5;10]
27 [5;5,10]
28 [5;3,2,3,10]
29 [5;2,1,1,2,10]
30 [5;2,10]
31 [5;1,1,3,5,3,1,1,10]
32 [5;1,1,1,10]
33 [5;1,2,1,10]
34 [5;1,4,1,10]
35 [5;1,10]
36 [6]

Squares have a period of length 0. The last term in a period is 2*floor(sqrt(n)). The remaining terms of a period are mirrored at the center or the middle.

Continued fractions of sqrt(n) and numerators/denominators of their convergents

n = 2 (A040000 and A001333/A000129), 3 (A040001 and A002531/A002530), 5 (A040002 and A001077/A001076), 6 (A040003 and A041006/A041007), 7 (A010121 and A041008/A041009), 8 (A040005 and A041010/A041011), 10 (A040006 and A005667/A005668), 11 (A040007 and A041014/A041015), 12 (A040008 and A041016/A041017), 13 (A010122 and A041018/A041019), 14 (A010123 and A041020/A041021), 15 (A040011 and A041022/A041023), 17 (A040012 and A041024/A041025), 18 (A040013 and A041026/A041027), 19 (A010124 and A041028/A041029), 20 (A040015 and A041030/A041031), 21 (A010125 and A041032/A041033), 22 (A010126 and A041034/A041035), 23 (A010127 and A041036/A041037), 24 (A040019 and A041038/A041039), 26 (A040020 and A041040/A041041), 27 (A040021 and A041042/A041043), 28 (A040022 and A041044/A041045), 29 (A010128 and A041046/A041047), 30 (A040024 and A041048/A041049), 31 (A010129 and A041050/A041051), 32 (A010130 and A041052/A041053), 33 (A010131 and A041054/A041055), 34 (A010132 and A041056/A041057), 35 (A040029 and A041058/A041059), 37 (A040030 and A041060/A041061), 38 (A040031 and A041062/A041063), 39 (A040032 and A041064/A041065), 40 (A040033 and A041066/A041067), 41 (A010133 and A041068/A041069), 42 (A040035 and A041070/A041071), 43 (A010134 and A041072/A041073), 44 (A040037 and A041074/A041075), 45 (A010135 and A041076/A041077), 46 (A010136 and A041078/A041079), 47 (A010137 and A041080/A041081), 48 (A040041 and A041082/A041083), 50 (A040042 and A041084/A041085), 51 (A040043 and A041086/A041087), 52 (A010138 and A041088/A041089), 53 (A010139 and A041090/A041091), 54 (A010140 and A041092/A041093), 55 (A010141 and A041094/A041095), 56 (A040048 and A041096/A041097), 57 (A010142 and A041098/A041099), 58 (A010143 and A041100/A041101), 59 (A010144 and A041102/A041103), 60 (A040052 and A041104/A041105), 61 (A010145 and A041106/A041107), 62 (A010146 and A041108/A041109), 63 (A040055 and A041110/A041111), 65 (A040056 and A041112/A041113), 66 (A040057 and A041114/A041115), 67 (A010147 and A041116/A041117), 68 (A040059 and A041118/A041119), 69 (A010148 and A041120/A041121), 70 (A010149 and A041122/A041123), 71 (A010150 and A041124/A041125), 72 (A040063 and A041126/A041127), 73 (A010151 and A041128/A041129), 74 (A010152 and A041130/A041131), 75 (A010153 and A041132/A041133), 76 (A010154 and A041134/A041135), 77 (A010155 and A041136/A041137), 78 (A010156 and A041138/A041139), 79 (A010157 and A041140/A041141), 80 (A040071 and A041142/A041143), 82 (A040072 and A041144/A041145), 83 (A040073 and A041146/A041147), 84 (A040074 and A041148/A041149), 85 (A010158 and A041150/A041151), 86 (A010159 and A041152/A041153), 87 (A040077 and A041154/A041155), 88 (A010160 and A041156/A041157), 89 (A010161 and A041158/A041159), 90 (A040080 and A041160/A041161), 91 (A010162 and A041162/A041163), 92 (A010163 and A041164/A041165), 93 (A010164 and A041166/A041167), 94 (A010165 and A041168/A041169), 95 (A010166 and A041170/A041171), 96 (A010167 and A041172/A041173), 97 (A010168 and A041174/A041175), 98 (A010169 and A041176/A041177), 99 (A010170 and A041178/A041179),

101 (A040090 and A041180/A041181), 102 (A040091 and A041182/A041183), 103 (A010171 and A041184/A041185), 104 (A040093 and A041186/A041187), 105 (A040094 and A041188/A041189), 106 (A010172 and A041190/A041191), 107 (A010173 and A041192/A041193), 108 (A010174 and A041194/A041195), 109 (A010175 and A041196/A041197), 110 (A040099 and A041198/A041199), 111 (A010176 and A041200/A041201), 112 (A010177 and A041202/A041203), 113 (A010178 and A041204/A041205), 114 (A010179 and A041206/A041207), 115 (A010180 and A041208/A041209), 116 (A010181 and A041210/A041211), 117 (A010182 and A041212/A041213), 118 (A010183 and A041214/A041215), 119 (A010184 and A041216/A041217), 120 (A040109 and A041218/A041219), 122 (A040110 and A041220/A041221), 123 (A040111 and A041222/A041223), 124 (A010185 and A041224/A041225), 125 (A010186 and A041226/A041227), 126 (A010187 and A041228/A041229), 127 (A010188 and A041230/A041231), 128 (A010189 and A041232/A041233), 129 (A010190 and A041234/A041235), 130 (A040118 and A041236/A041237), 131 (A010191 and A041238/A041239), 132 (A040120 and A041240/A041241), 133 (A010192 and A041242/A041243), 134 (A010193 and A041244/A041245), 135 (A010194 and A041246/A041247), 136 (A010195 and A041248/A041249), 137 (A010196 and A041250/A041251), 138 (A010197 and A041252/A041253), 139 (A010198 and A041254/A041255), 140 (A010199 and A041256/A041257), 141 (A010200 and A041258/A041259), 142 (A010201 and A041260/A041261), 143 (A040131 and A041262/A041263), 145 (A040132 and A041264/A041265), 146 (A040133 and A041266/A041267), 147 (A040134 and A041268/A041269), 148 (A040135 and A041270/A041271), 149 (A010202 and A041272/A041273), 150 (A040137 and A041274/A041275), 151 (A010203 and A041276/A041277), 152 (A040139 and A041278/A041279), 153 (A010204 and A041280/A041281), 154 (A010205 and A041282/A041283), 155 (A040142 and A041284/A041285), 156 (A040143 and A041286/A041287), 157 (A010206 and A041288/A041289), 158 (A010207 and A041290/A041291), 159 (A010208 and A041292/A041293), 160 (A010209 and A041294/A041295), 161 (A010210 and A041296/A041297), 162 (A010211 and A041298/A001112), 163 (A010212 and A041300/A041301), 164 (A040151 and A041302/A041303), 165 (A010213 and A041304/A041305), 166 (A010214 and A041306/A041307), 167 (A010215 and A041308/A041309), 168 (A040155 and A041310/A041311), 170 (A040156 and A041312/A041313), 171 (A040157 and A041314/A041315), 172 (A010216 and A041316/A041317), 173 (A010217 and A041318/A041319), 174 (A010218 and A041320/A041321), 175 (A010219 and A041322/A041323), 176 (A010220 and A041324/A041325), 177 (A010221 and A041326/A041327), 178 (A010222 and A041328/A041329), 179 (A010223 and A041330/A041331), 180 (A040166 and A041332/A041333), 181 (A010224 and A041334/A041335), 182 (A040168 and A041336/A041337), 183 (A010225 and A041338/A041339), 184 (A010226 and A041340/A041341), 185 (A010227 and A041342/A041343), 186 (A010228 and A041344/A041345), 187 (A010229 and A041346/A041347), 188 (A010230 and A041348/A041349), 189 (A010231 and A041350/A041351), 190 (A010232 and A041352/A041353), 191 (A010233 and A041354/A041355), 192 (A010234 and A041356/A041357), 193 (A010235 and A041358/A041359), 194 (A010236 and A041360/A041361), 195 (A040181 and A041362/A041363), 197 (A040182 and A041364/A041365), 198 (A040183 and A041366/A041367), 199 (A010237 and A041368/A041369),

200 (A040185 and A041370/A041371), 201 (A040186 and A041372/A041373), 202 (A040187 and A041374/A041375), 203 (A040188 and A041376/A041377), 204 (A040189 and A041378/A041379), 205 (A040190 and A041380/A041381), 206 (A040191 and A041382/A041383), 207 (A040192 and A041384/A041385), 208 (A040193 and A041386/A041387), 209 (A040194 and A041388/A041389), 210 (A040195 and A041390/A041391), 211 (A040196 and A041392/A041393), 212 (A040197 and A041394/A041395), 213 (A040198 and A041396/A041397), 214 (A040199 and A041398/A041399), 215 (A040200 and A041400/A041401), 216 (A040201 and A041402/A041403), 217 (A040202 and A041404/A041405), 218 (A040203 and A041406/A041407), 219 (A040204 and A041408/A041409), 220 (A040205 and A041410/A041411), 221 (A040206 and A041412/A041413), 222 (A040207 and A041414/A041415), 223 (A040208 and A041416/A041417), 224 (A040209 and A041418/A041419), 226 (A040210 and A041420/A041421), 227 (A040211 and A041422/A041423), 228 (A040212 and A041424/A041425), 229 (A040213 and A041426/A041427), 230 (A040214 and A041428/A041429), 231 (A040215 and A041430/A041431), 232 (A040216 and A041432/A041433), 233 (A040217 and A041434/A041435), 234 (A040218 and A041436/A041437), 235 (A040219 and A041438/A041439), 236 (A040220 and A041440/A041441), 237 (A040221 and A041442/A041443), 238 (A040222 and A041444/A041445), 239 (A040223 and A041446/A041447), 240 (A040224 and A041448/A041449), 241 (A040225 and A041450/A041451), 242 (A040226 and A041452/A041453), 243 (A040227 and A041454/A041455), 244 (A040228 and A041456/A041457), 245 (A040229 and A041458/A041459), 246 (A040230 and A041460/A041461), 247 (A040231 and A041462/A041463), 248 (A040232 and A041464/A041465), 249 (A040233 and A041466/A041467), 250 (A040234 and A041468/A041469), 251 (A040235 and A041470/A041471), 252 (A040236 and A041472/A041473), 253 (A040237 and A041474/A041475), 254 (A040238 and A041476/A041477), 255 (A040239 and A041478/A041479), 257 (A040240 and A041480/A041481), 258 (A040241 and A041482/A041483), 259 (A040242 and A041484/A041485), 260 (A040243 and A041486/A041487), 261 (A040244 and A041488/A041489), 262 (A040245 and A041490/A041491), 263 (A040246 and A041492/A041493), 264 (A040247 and A041494/A041495), 265 (A040248 and A041496/A041497), 266 (A040249 and A041498/A041499), 267 (A040250 and A041500/A041501), 268 (A040251 and A041502/A041503), 269 (A040252 and A041504/A041505), 270 (A040253 and A041506/A041507), 271 (A040254 and A041508/A041509), 272 (A040255 and A041510/A041511), 273 (A040256 and A041512/A041513), 274 (A040257 and A041514/A041515), 275 (A040258 and A041516/A041517), 276 (A040259 and A041518/A041519), 277 (A040260 and A041520/A041521), 278 (A040261 and A041522/A041523), 279 (A040262 and A041524/A041525), 280 (A040263 and A041526/A041527), 281 (A040264 and A041528/A041529), 282 (A040265 and A041530/A041531), 283 (A040266 and A041532/A041533), 284 (A040267 and A041534/A041535), 285 (A040268 and A041536/A041537), 286 (A040269 and A041538/A041539), 287 (A040270 and A041540/A041541), 288 (A040271 and A041542/A041543), 290 (A040272 and A041544/A041545), 291 (A040273 and A041546/A041547), 292 (A040274 and A041548/A041549), 293 (A040275 and A041550/A041551), 294 (A040276 and A041552/A041553), 295 (A040277 and A041554/A041555), 296 (A040278 and A041556/A041557), 297 (A040279 and A041558/A041559), 298 (A040280 and A041560/A041561), 299 (A040281 and A041562/A041563),

300 (A040282 and A041564/A041565), 301 (A040283 and A041566/A041567), 302 (A040284 and A041568/A041569), 303 (A040285 and A041570/A041571), 304 (A040286 and A041572/A041573), 305 (A040287 and A041574/A041575), 306 (A040288 and A041576/A041577), 307 (A040289 and A041578/A041579), 308 (A040290 and A041580/A041581), 309 (A040291 and A041582/A041583), 310 (A040292 and A041584/A041585), 311 (A040293 and A041586/A041587), 312 (A040294 and A041588/A041589), 313 (A040295 and A041590/A041591), 314 (A040296 and A041592/A041593), 315 (A040297 and A041594/A041595), 316 (A040298 and A041596/A041597), 317 (A040299 and A041598/A041599), 318 (A040300 and A041600/A041601), 319 (A040301 and A041602/A041603), 320 (A040302 and A041604/A041605), 321 (A040303 and A041606/A041607), 322 (A040304 and A041608/A041609), 323 (A040305 and A041610/A041611), 325 (A040306 and A041612/A041613), 326 (A040307 and A041614/A041615), 327 (A040308 and A041616/A041617), 328 (A040309 and A041618/A041619), 329 (A040310 and A041620/A041621), 330 (A040311 and A041622/A041623), 331 (A040312 and A041624/A041625), 332 (A040313 and A041626/A041627), 333 (A040314 and A041628/A041629), 334 (A040315 and A041630/A041631), 335 (A040316 and A041632/A041633), 336 (A040317 and A041634/A041635), 337 (A040318 and A041636/A041637), 338 (A040319 and A041638/A041639), 339 (A040320 and A041640/A041641), 340 (A040321 and A041642/A041643), 341 (A040322 and A041644/A041645), 342 (A040323 and A041646/A041647), 343 (A040324 and A041648/A041649), 344 (A040325 and A041650/A041651), 345 (A040326 and A041652/A041653), 346 (A040327 and A041654/A041655), 347 (A040328 and A041656/A041657), 348 (A040329 and A041658/A041659), 349 (A040330 and A041660/A041661), 350 (A040331 and A041662/A041663), 351 (A040332 and A041664/A041665), 352 (A040333 and A041666/A041667), 353 (A040334 and A041668/A041669), 354 (A040335 and A041670/A041671), 355 (A040336 and A041672/A041673), 356 (A040337 and A041674/A041675), 357 (A040338 and A041676/A041677), 358 (A040339 and A041678/A041679), 359 (A040340 and A041680/A041681), 360 (A040341 and A041682/A041683), 362 (A040342 and A041684/A041685), 363 (A040343 and A041686/A041687), 364 (A040344 and A041688/A041689), 365 (A040345 and A041690/A041691), 366 (A040346 and A041692/A041693), 367 (A040347 and A041694/A041695), 368 (A040348 and A041696/A041697), 369 (A040349 and A041698/A041699), 370 (A040350 and A041700/A041701), 371 (A040351 and A041702/A041703), 372 (A040352 and A041704/A041705), 373 (A040353 and A041706/A041707), 374 (A040354 and A041708/A041709), 375 (A040355 and A041710/A041711), 376 (A040356 and A041712/A041713), 377 (A040357 and A041714/A041715), 378 (A040358 and A041716/A041717), 379 (A040359 and A041718/A041719), 380 (A040360 and A041720/A041721), 381 (A040361 and A041722/A041723), 382 (A040362 and A041724/A041725), 383 (A040363 and A041726/A041727), 384 (A040364 and A041728/A041729), 385 (A040365 and A041730/A041731), 386 (A040366 and A041732/A041733), 387 (A040367 and A041734/A041735), 388 (A040368 and A041736/A041737), 389 (A040369 and A041738/A041739), 390 (A040370 and A041740/A041741), 391 (A040371 and A041742/A041743), 392 (A040372 and A041744/A041745), 393 (A040373 and A041746/A041747), 394 (A040374 and A041748/A041749), 395 (A040375 and A041750/A041751), 396 (A040376 and A041752/A041753), 397 (A040377 and A041754/A041755), 398 (A040378 and A041756/A041757), 399 (A040379 and A041758/A041759),

401 (A040380 and A041760/A041761), 402 (A040381 and A041762/A041763), 403 (A040382 and A041764/A041765), 404 (A040383 and A041766/A041767), 405 (A040384 and A041768/A041769), 406 (A040385 and A041770/A041771), 407 (A040386 and A041772/A041773), 408 (A040387 and A041774/A041775), 409 (A040388 and A041776/A041777), 410 (A040389 and A041778/A041779), 411 (A040390 and A041780/A041781), 412 (A040391 and A041782/A041783), 413 (A040392 and A041784/A041785), 414 (A040393 and A041786/A041787), 415 (A040394 and A041788/A041789), 416 (A040395 and A041790/A041791), 417 (A040396 and A041792/A041793), 418 (A040397 and A041794/A041795), 419 (A040398 and A041796/A041797), 420 (A040399 and A041798/A041799), 421 (A040400 and A041800/A041801), 422 (A040401 and A041802/A041803), 423 (A040402 and A041804/A041805), 424 (A040403 and A041806/A041807), 425 (A040404 and A041808/A041809), 426 (A040405 and A041810/A041811), 427 (A040406 and A041812/A041813), 428 (A040407 and A041814/A041815), 429 (A040408 and A041816/A041817), 430 (A040409 and A041818/A041819), 431 (A040410 and A041820/A041821), 432 (A040411 and A041822/A041823), 433 (A040412 and A041824/A041825), 434 (A040413 and A041826/A041827), 435 (A040414 and A041828/A041829), 436 (A040415 and A041830/A041831), 437 (A040416 and A041832/A041833), 438 (A040417 and A041834/A041835), 439 (A040418 and A041836/A041837), 440 (A040419 and A041838/A041839), 442 (A040420 and A041840/A041841), 443 (A040421 and A041842/A041843), 444 (A040422 and A041844/A041845), 445 (A040423 and A041846/A041847), 446 (A040424 and A041848/A041849), 447 (A040425 and A041850/A041851), 448 (A040426 and A041852/A041853), 449 (A040427 and A041854/A041855), 450 (A040428 and A041856/A041857), 451 (A040429 and A041858/A041859), 452 (A040430 and A041860/A041861), 453 (A040431 and A041862/A041863), 454 (A040432 and A041864/A041865), 455 (A040433 and A041866/A041867), 456 (A040434 and A041868/A041869), 457 (A040435 and A041870/A041871), 458 (A040436 and A041872/A041873), 459 (A040437 and A041874/A041875), 460 (A040438 and A041876/A041877), 461 (A040439 and A041878/A041879), 462 (A040440 and A041880/A041881), 463 (A040441 and A041882/A041883), 464 (A040442 and A041884/A041885), 465 (A040443 and A041886/A041887), 466 (A040444 and A041888/A041889), 467 (A040445 and A041890/A041891), 468 (A040446 and A041892/A041893), 469 (A040447 and A041894/A041895), 470 (A040448 and A041896/A041897), 471 (A040449 and A041898/A041899), 472 (A040450 and A041900/A041901), 473 (A040451 and A041902/A041903), 474 (A040452 and A041904/A041905), 475 (A040453 and A041906/A041907), 476 (A040454 and A041908/A041909), 477 (A040455 and A041910/A041911), 478 (A040456 and A041912/A041913), 479 (A040457 and A041914/A041915), 480 (A040458 and A041916/A041917), 481 (A040459 and A041918/A041919), 482 (A040460 and A041920/A041921), 483 (A040461 and A041922/A041923), 485 (A040462 and A041924/A041925), 486 (A040463 and A041926/A041927), 487 (A040464 and A041928/A041929), 488 (A040465 and A041930/A041931), 489 (A040466 and A041932/A041933), 490 (A040467 and A041934/A041935), 491 (A040468 and A041936/A041937), 492 (A040469 and A041938/A041939), 493 (A040470 and A041940/A041941), 494 (A040471 and A041942/A041943), 495 (A040472 and A041944/A041945), 496 (A040473 and A041946/A041947), 497 (A040474 and A041948/A041949), 498 (A040475 and A041950/A041951), 499 (A040476 and A041952/A041953),

500 (A040477 and A041954/A041955), 501 (A040478 and A041956/A041957), 502 (A040479 and A041958/A041959), 503 (A040480 and A041960/A041961), 504 (A040481 and A041962/A041963), 505 (A040482 and A041964/A041965), 506 (A040483 and A041966/A041967), 507 (A040484 and A041968/A041969), 508 (A040485 and A041970/A041971), 509 (A040486 and A041972/A041973), 510 (A040487 and A041974/A041975), 511 (A040488 and A041976/A041977), 512 (A040489 and A041978/A041979), 513 (A040490 and A041980/A041981), 514 (A040491 and A041982/A041983), 515 (A040492 and A041984/A041985), 516 (A040493 and A041986/A041987), 517 (A040494 and A041988/A041989), 518 (A040495 and A041990/A041991), 519 (A040496 and A041992/A041993), 520 (A040497 and A041994/A041995), 521 (A040498 and A041996/A041997), 522 (A040499 and A041998/A041999), 523 (A040500 and A042000/A042001), 524 (A040501 and A042002/A042003), 525 (A040502 and A042004/A042005), 526 (A040503 and A042006/A042007), 527 (A040504 and A042008/A042009), 528 (A040505 and A042010/A042011), 530 (A040506 and A042012/A042013), 531 (A040507 and A042014/A042015), 532 (A040508 and A042016/A042017), 533 (A040509 and A042018/A042019), 534 (A040510 and A042020/A042021), 535 (A040511 and A042022/A042023), 536 (A040512 and A042024/A042025), 537 (A040513 and A042026/A042027), 538 (A040514 and A042028/A042029), 539 (A040515 and A042030/A042031), 540 (A040516 and A042032/A042033), 541 (A040517 and A042034/A042035), 542 (A040518 and A042036/A042037), 543 (A040519 and A042038/A042039), 544 (A040520 and A042040/A042041), 545 (A040521 and A042042/A042043), 546 (A040522 and A042044/A042045), 547 (A040523 and A042046/A042047), 548 (A040524 and A042048/A042049), 549 (A040525 and A042050/A042051), 550 (A040526 and A042052/A042053), 551 (A040527 and A042054/A042055), 552 (A040528 and A042056/A042057), 553 (A040529 and A042058/A042059), 554 (A040530 and A042060/A042061), 555 (A040531 and A042062/A042063), 556 (A040532 and A042064/A042065), 557 (A040533 and A042066/A042067), 558 (A040534 and A042068/A042069), 559 (A040535 and A042070/A042071), 560 (A040536 and A042072/A042073), 561 (A040537 and A042074/A042075), 562 (A040538 and A042076/A042077), 563 (A040539 and A042078/A042079), 564 (A040540 and A042080/A042081), 565 (A040541 and A042082/A042083), 566 (A040542 and A042084/A042085), 567 (A040543 and A042086/A042087), 568 (A040544 and A042088/A042089), 569 (A040545 and A042090/A042091), 570 (A040546 and A042092/A042093), 571 (A040547 and A042094/A042095), 572 (A040548 and A042096/A042097), 573 (A040549 and A042098/A042099), 574 (A040550 and A042100/A042101), 575 (A040551 and A042102/A042103), 577 (A040552 and A042104/A042105), 578 (A040553 and A042106/A042107), 579 (A040554 and A042108/A042109), 580 (A040555 and A042110/A042111), 581 (A040556 and A042112/A042113), 582 (A040557 and A042114/A042115), 583 (A040558 and A042116/A042117), 584 (A040559 and A042118/A042119), 585 (A040560 and A042120/A042121), 586 (A040561 and A042122/A042123), 587 (A040562 and A042124/A042125), 588 (A040563 and A042126/A042127), 589 (A040564 and A042128/A042129), 590 (A040565 and A042130/A042131), 591 (A040566 and A042132/A042133), 592 (A040567 and A042134/A042135), 593 (A040568 and A042136/A042137), 594 (A040569 and A042138/A042139), 595 (A040570 and A042140/A042141), 596 (A040571 and A042142/A042143), 597 (A040572 and A042144/A042145), 598 (A040573 and A042146/A042147), 599 (A040574 and A042148/A042149),

600 (A040575 and A042150/A042151), 601 (A040576 and A042152/A042153), 602 (A040577 and A042154/A042155), 603 (A040578 and A042156/A042157), 604 (A040579 and A042158/A042159), 605 (A040580 and A042160/A042161), 606 (A040581 and A042162/A042163), 607 (A040582 and A042164/A042165), 608 (A040583 and A042166/A042167), 609 (A040584 and A042168/A042169), 610 (A040585 and A042170/A042171), 611 (A040586 and A042172/A042173), 612 (A040587 and A042174/A042175), 613 (A040588 and A042176/A042177), 614 (A040589 and A042178/A042179), 615 (A040590 and A042180/A042181), 616 (A040591 and A042182/A042183), 617 (A040592 and A042184/A042185), 618 (A040593 and A042186/A042187), 619 (A040594 and A042188/A042189), 620 (A040595 and A042190/A042191), 621 (A040596 and A042192/A042193), 622 (A040597 and A042194/A042195), 623 (A040598 and A042196/A042197), 624 (A040599 and A042198/A042199), 626 (A040600 and A042200/A042201), 627 (A040601 and A042202/A042203), 628 (A040602 and A042204/A042205), 629 (A040603 and A042206/A042207), 630 (A040604 and A042208/A042209), 631 (A040605 and A042210/A042211), 632 (A040606 and A042212/A042213), 633 (A040607 and A042214/A042215), 634 (A040608 and A042216/A042217), 635 (A040609 and A042218/A042219), 636 (A040610 and A042220/A042221), 637 (A040611 and A042222/A042223), 638 (A040612 and A042224/A042225), 639 (A040613 and A042226/A042227), 640 (A040614 and A042228/A042229), 641 (A040615 and A042230/A042231), 642 (A040616 and A042232/A042233), 643 (A040617 and A042234/A042235), 644 (A040618 and A042236/A042237), 645 (A040619 and A042238/A042239), 646 (A040620 and A042240/A042241), 647 (A040621 and A042242/A042243), 648 (A040622 and A042244/A042245), 649 (A040623 and A042246/A042247), 650 (A040624 and A042248/A042249), 651 (A040625 and A042250/A042251), 652 (A040626 and A042252/A042253), 653 (A040627 and A042254/A042255), 654 (A040628 and A042256/A042257), 655 (A040629 and A042258/A042259), 656 (A040630 and A042260/A042261), 657 (A040631 and A042262/A042263), 658 (A040632 and A042264/A042265), 659 (A040633 and A042266/A042267), 660 (A040634 and A042268/A042269), 661 (A040635 and A042270/A042271), 662 (A040636 and A042272/A042273), 663 (A040637 and A042274/A042275), 664 (A040638 and A042276/A042277), 665 (A040639 and A042278/A042279), 666 (A040640 and A042280/A042281), 667 (A040641 and A042282/A042283), 668 (A040642 and A042284/A042285), 669 (A040643 and A042286/A042287), 670 (A040644 and A042288/A042289), 671 (A040645 and A042290/A042291), 672 (A040646 and A042292/A042293), 673 (A040647 and A042294/A042295), 674 (A040648 and A042296/A042297), 675 (A040649 and A042298/A042299), 677 (A040650 and A042300/A042301), 678 (A040651 and A042302/A042303), 679 (A040652 and A042304/A042305), 680 (A040653 and A042306/A042307), 681 (A040654 and A042308/A042309), 682 (A040655 and A042310/A042311), 683 (A040656 and A042312/A042313), 684 (A040657 and A042314/A042315), 685 (A040658 and A042316/A042317), 686 (A040659 and A042318/A042319), 687 (A040660 and A042320/A042321), 688 (A040661 and A042322/A042323), 689 (A040662 and A042324/A042325), 690 (A040663 and A042326/A042327), 691 (A040664 and A042328/A042329), 692 (A040665 and A042330/A042331), 693 (A040666 and A042332/A042333), 694 (A040667 and A042334/A042335), 695 (A040668 and A042336/A042337), 696 (A040669 and A042338/A042339), 697 (A040670 and A042340/A042341), 698 (A040671 and A042342/A042343), 699 (A040672 and A042344/A042345),

700 (A040673 and A042346/A042347), 701 (A040674 and A042348/A042349), 702 (A040675 and A042350/A042351), 703 (A040676 and A042352/A042353), 704 (A040677 and A042354/A042355), 705 (A040678 and A042356/A042357), 706 (A040679 and A042358/A042359), 707 (A040680 and A042360/A042361), 708 (A040681 and A042362/A042363), 709 (A040682 and A042364/A042365), 710 (A040683 and A042366/A042367), 711 (A040684 and A042368/A042369), 712 (A040685 and A042370/A042371), 713 (A040686 and A042372/A042373), 714 (A040687 and A042374/A042375), 715 (A040688 and A042376/A042377), 716 (A040689 and A042378/A042379), 717 (A040690 and A042380/A042381), 718 (A040691 and A042382/A042383), 719 (A040692 and A042384/A042385), 720 (A040693 and A042386/A042387), 721 (A040694 and A042388/A042389), 722 (A040695 and A042390/A042391), 723 (A040696 and A042392/A042393), 724 (A040697 and A042394/A042395), 725 (A040698 and A042396/A042397), 726 (A040699 and A042398/A042399), 727 (A040700 and A042400/A042401), 728 (A040701 and A042402/A042403), 730 (A040702 and A042404/A042405), 731 (A040703 and A042406/A042407), 732 (A040704 and A042408/A042409), 733 (A040705 and A042410/A042411), 734 (A040706 and A042412/A042413), 735 (A040707 and A042414/A042415), 736 (A040708 and A042416/A042417), 737 (A040709 and A042418/A042419), 738 (A040710 and A042420/A042421), 739 (A040711 and A042422/A042423), 740 (A040712 and A042424/A042425), 741 (A040713 and A042426/A042427), 742 (A040714 and A042428/A042429), 743 (A040715 and A042430/A042431), 744 (A040716 and A042432/A042433), 745 (A040717 and A042434/A042435), 746 (A040718 and A042436/A042437), 747 (A040719 and A042438/A042439), 748 (A040720 and A042440/A042441), 749 (A040721 and A042442/A042443), 750 (A040722 and A042444/A042445), 751 (A040723 and A042446/A042447), 752 (A040724 and A042448/A042449), 753 (A040725 and A042450/A042451), 754 (A040726 and A042452/A042453), 755 (A040727 and A042454/A042455), 756 (A040728 and A042456/A042457), 757 (A040729 and A042458/A042459), 758 (A040730 and A042460/A042461), 759 (A040731 and A042462/A042463), 760 (A040732 and A042464/A042465), 761 (A040733 and A042466/A042467), 762 (A040734 and A042468/A042469), 763 (A040735 and A042470/A042471), 764 (A040736 and A042472/A042473), 765 (A040737 and A042474/A042475), 766 (A040738 and A042476/A042477), 767 (A040739 and A042478/A042479), 768 (A040740 and A042480/A042481), 769 (A040741 and A042482/A042483), 770 (A040742 and A042484/A042485), 771 (A040743 and A042486/A042487), 772 (A040744 and A042488/A042489), 773 (A040745 and A042490/A042491), 774 (A040746 and A042492/A042493), 775 (A040747 and A042494/A042495), 776 (A040748 and A042496/A042497), 777 (A040749 and A042498/A042499), 778 (A040750 and A042500/A042501), 779 (A040751 and A042502/A042503), 780 (A040752 and A042504/A042505), 781 (A040753 and A042506/A042507), 782 (A040754 and A042508/A042509), 783 (A040755 and A042510/A042511), 785 (A040756 and A042512/A042513), 786 (A040757 and A042514/A042515), 787 (A040758 and A042516/A042517), 788 (A040759 and A042518/A042519), 789 (A040760 and A042520/A042521), 790 (A040761 and A042522/A042523), 791 (A040762 and A042524/A042525), 792 (A040763 and A042526/A042527), 793 (A040764 and A042528/A042529), 794 (A040765 and A042530/A042531), 795 (A040766 and A042532/A042533), 796 (A040767 and A042534/A042535), 797 (A040768 and A042536/A042537), 798 (A040769 and A042538/A042539), 799 (A040770 and A042540/A042541),

800 (A040771 and A042542/A042543), 801 (A040772 and A042544/A042545), 802 (A040773 and A042546/A042547), 803 (A040774 and A042548/A042549), 804 (A040775 and A042550/A042551), 805 (A040776 and A042552/A042553), 806 (A040777 and A042554/A042555), 807 (A040778 and A042556/A042557), 808 (A040779 and A042558/A042559), 809 (A040780 and A042560/A042561), 810 (A040781 and A042562/A042563), 811 (A040782 and A042564/A042565), 812 (A040783 and A042566/A042567), 813 (A040784 and A042568/A042569), 814 (A040785 and A042570/A042571), 815 (A040786 and A042572/A042573), 816 (A040787 and A042574/A042575), 817 (A040788 and A042576/A042577), 818 (A040789 and A042578/A042579), 819 (A040790 and A042580/A042581), 820 (A040791 and A042582/A042583), 821 (A040792 and A042584/A042585), 822 (A040793 and A042586/A042587), 823 (A040794 and A042588/A042589), 824 (A040795 and A042590/A042591), 825 (A040796 and A042592/A042593), 826 (A040797 and A042594/A042595), 827 (A040798 and A042596/A042597), 828 (A040799 and A042598/A042599), 829 (A040800 and A042600/A042601), 830 (A040801 and A042602/A042603), 831 (A040802 and A042604/A042605), 832 (A040803 and A042606/A042607), 833 (A040804 and A042608/A042609), 834 (A040805 and A042610/A042611), 835 (A040806 and A042612/A042613), 836 (A040807 and A042614/A042615), 837 (A040808 and A042616/A042617), 838 (A040809 and A042618/A042619), 839 (A040810 and A042620/A042621), 840 (A040811 and A042622/A042623), 842 (A040812 and A042624/A042625), 843 (A040813 and A042626/A042627), 844 (A040814 and A042628/A042629), 845 (A040815 and A042630/A042631), 846 (A040816 and A042632/A042633), 847 (A040817 and A042634/A042635), 848 (A040818 and A042636/A042637), 849 (A040819 and A042638/A042639), 850 (A040820 and A042640/A042641), 851 (A040821 and A042642/A042643), 852 (A040822 and A042644/A042645), 853 (A040823 and A042646/A042647), 854 (A040824 and A042648/A042649), 855 (A040825 and A042650/A042651), 856 (A040826 and A042652/A042653), 857 (A040827 and A042654/A042655), 858 (A040828 and A042656/A042657), 859 (A040829 and A042658/A042659), 860 (A040830 and A042660/A042661), 861 (A040831 and A042662/A042663), 862 (A040832 and A042664/A042665), 863 (A040833 and A042666/A042667), 864 (A040834 and A042668/A042669), 865 (A040835 and A042670/A042671), 866 (A040836 and A042672/A042673), 867 (A040837 and A042674/A042675), 868 (A040838 and A042676/A042677), 869 (A040839 and A042678/A042679), 870 (A040840 and A042680/A042681), 871 (A040841 and A042682/A042683), 872 (A040842 and A042684/A042685), 873 (A040843 and A042686/A042687), 874 (A040844 and A042688/A042689), 875 (A040845 and A042690/A042691), 876 (A040846 and A042692/A042693), 877 (A040847 and A042694/A042695), 878 (A040848 and A042696/A042697), 879 (A040849 and A042698/A042699), 880 (A040850 and A042700/A042701), 881 (A040851 and A042702/A042703), 882 (A040852 and A042704/A042705), 883 (A040853 and A042706/A042707), 884 (A040854 and A042708/A042709), 885 (A040855 and A042710/A042711), 886 (A040856 and A042712/A042713), 887 (A040857 and A042714/A042715), 888 (A040858 and A042716/A042717), 889 (A040859 and A042718/A042719), 890 (A040860 and A042720/A042721), 891 (A040861 and A042722/A042723), 892 (A040862 and A042724/A042725), 893 (A040863 and A042726/A042727), 894 (A040864 and A042728/A042729), 895 (A040865 and A042730/A042731), 896 (A040866 and A042732/A042733), 897 (A040867 and A042734/A042735), 898 (A040868 and A042736/A042737), 899 (A040869 and A042738/A042739),

901 (A040870 and A042740/A042741), 902 (A040871 and A042742/A042743), 903 (A040872 and A042744/A042745), 904 (A040873 and A042746/A042747), 905 (A040874 and A042748/A042749), 906 (A040875 and A042750/A042751), 907 (A040876 and A042752/A042753), 908 (A040877 and A042754/A042755), 909 (A040878 and A042756/A042757), 910 (A040879 and A042758/A042759), 911 (A040880 and A042760/A042761), 912 (A040881 and A042762/A042763), 913 (A040882 and A042764/A042765), 914 (A040883 and A042766/A042767), 915 (A040884 and A042768/A042769), 916 (A040885 and A042770/A042771), 917 (A040886 and A042772/A042773), 918 (A040887 and A042774/A042775), 919 (A040888 and A042776/A042777), 920 (A040889 and A042778/A042779), 921 (A040890 and A042780/A042781), 922 (A040891 and A042782/A042783), 923 (A040892 and A042784/A042785), 924 (A040893 and A042786/A042787), 925 (A040894 and A042788/A042789), 926 (A040895 and A042790/A042791), 927 (A040896 and A042792/A042793), 928 (A040897 and A042794/A042795), 929 (A040898 and A042796/A042797), 930 (A040899 and A042798/A042799), 931 (A040900 and A042800/A042801), 932 (A040901 and A042802/A042803), 933 (A040902 and A042804/A042805), 934 (A040903 and A042806/A042807), 935 (A040904 and A042808/A042809), 936 (A040905 and A042810/A042811), 937 (A040906 and A042812/A042813), 938 (A040907 and A042814/A042815), 939 (A040908 and A042816/A042817), 940 (A040909 and A042818/A042819), 941 (A040910 and A042820/A042821), 942 (A040911 and A042822/A042823), 943 (A040912 and A042824/A042825), 944 (A040913 and A042826/A042827), 945 (A040914 and A042828/A042829), 946 (A040915 and A042830/A042831), 947 (A040916 and A042832/A042833), 948 (A040917 and A042834/A042835), 949 (A040918 and A042836/A042837), 950 (A040919 and A042838/A042839), 951 (A040920 and A042840/A042841), 952 (A040921 and A042842/A042843), 953 (A040922 and A042844/A042845), 954 (A040923 and A042846/A042847), 955 (A040924 and A042848/A042849), 956 (A040925 and A042850/A042851), 957 (A040926 and A042852/A042853), 958 (A040927 and A042854/A042855), 959 (A040928 and A042856/A042857), 960 (A040929 and A042858/A042859), 962 (A040930 and A042860/A042861), 963 (A040931 and A042862/A042863), 964 (A040932 and A042864/A042865), 965 (A040933 and A042866/A042867), 966 (A040934 and A042868/A042869), 967 (A040935 and A042870/A042871), 968 (A040936 and A042872/A042873), 969 (A040937 and A042874/A042875), 970 (A040938 and A042876/A042877), 971 (A040939 and A042878/A042879), 972 (A040940 and A042880/A042881), 973 (A040941 and A042882/A042883), 974 (A040942 and A042884/A042885), 975 (A040943 and A042886/A042887), 976 (A040944 and A042888/A042889), 977 (A040945 and A042890/A042891), 978 (A040946 and A042892/A042893), 979 (A040947 and A042894/A042895), 980 (A040948 and A042896/A042897), 981 (A040949 and A042898/A042899), 982 (A040950 and A042900/A042901), 983 (A040951 and A042902/A042903), 984 (A040952 and A042904/A042905), 985 (A040953 and A042906/A042907), 986 (A040954 and A042908/A042909), 987 (A040955 and A042910/A042911), 988 (A040956 and A042912/A042913), 989 (A040957 and A042914/A042915), 990 (A040958 and A042916/A042917), 991 (A040959 and A042918/A042919), 992 (A040960 and A042920/A042921), 993 (A040961 and A042922/A042923), 994 (A040962 and A042924/A042925), 995 (A040963 and A042926/A042927), 996 (A040964 and A042928/A042929), 997 (A040965 and A042930/A042931), 998 (A040966 and A042932/A042933), 999 (A040967 and A042934/A042935), 1000 (A040968 and A042936/A042937),

1729 (A053342).

Other quadratic irrationals

golden ratio (A000012)

sqrt(3) - 1 (A134451 and A048878/A002530)

Period length of continued fraction for square root of n

A003285 (0 if n is a square), A097853 (1 if n is a square)

sqrt(k) has a period of length m

m = 11 (A031779), 12 (A031780), 13 (A031781), 14 (A031782), 15 (A031783), 16 (A031784), 17 (A031785), 18 (A031786), 19 (A031787), 20 (A031788), 21 (A031789), 22 (A031790), 23 (A031791), 24 (A031792), 25 (A031793), 26 (A031794), 27 (A031795), 28 (A031796), 29 (A031797), 30 (A031798), 31 (A031799), 32 (A031800), 33 (A031801), 34 (A031802), 35 (A031803), 36 (A031804), 37 (A031805), 38 (A031806), 39 (A031807), 40 (A031808), 41 (A031809), 42 (A031810), 43 (A031811), 44 (A031812), 45 (A031813), 46 (A031814), 47 (A031815), 48 (A031816), 49 (A031817), 50 (A031818), 51 (A031819), 52 (A031820), 53 (A031821), 54 (A031822), 55 (A031823), 56 (A031824), 57 (A031825), 58 (A031826), 59 (A031827), 60 (A031828), 61 (A031829), 62 (A031830), 63 (A031831), 64 (A031832), 65 (A031833), 66 (A031834), 67 (A031835), 68 (A031836), 69 (A031837), 70 (A031838), 71 (A031839), 72 (A031840), 73 (A031841), 74 (A031842), 75 (A031843), 76 (A031844), 77 (A031845), 78 (A031846), 79 (A031847), 80 (A031848), 81 (A031849), 82 (A031850), 83 (A031851), 84 (A031852), 85 (A031853), 86 (A031854), 87 (A031855), 88 (A031856), 89 (A031857), 90 (A031858), 91 (A031859), 92 (A031860), 93 (A031861), 94 (A031862), 95 (A031863), 96 (A031864), 97 (A031865), 98 (A031866), 99 (A031867), 100 (A031868)

Period of continued fraction for sqrt(k) contains exactly m 1's

m = 0 (A013647), 1 (A013648), 2 (A013649), 3 (A013650), 4 (A020440), 5 (A020441), 6 (A020442), 7 (A020443), 8 (A020444), 9 (A020445), 10 (A020446), 11 (A031779), 12 (A031780), 13 (A031781), 14 (A031782), 15 (A031783), 16 (A031784), 17 (A031785), 18 (A031786), 19 (A031787), 20 (A031788), 21 (A031789), 22 (A031790), 23 (A031791), 24 (A031792), 25 (A031793), 26 (A031794), 27 (A031795), 28 (A031796), 29 (A031797), 30 (A031798), 31 (A031799), 32 (A031800), 33 (A031801), 34 (A031802), 35 (A031803), 36 (A031804), 37 (A031805), 38 (A031806), 39 (A031807), 40 (A031808), 41 (A031809), 42 (A031810), 43 (A031811), 44 (A031812), 45 (A031813), 46 (A031814), 47 (A031815), 48 (A031816), 49 (A031817), 50 (A031818), 51 (A031819), 52 (A031820), 53 (A031821), 54 (A031822), 55 (A031823), 56 (A031824), 57 (A031825), 58 (A031826), 59 (A031827), 60 (A031828), 61 (A031829), 62 (A031830), 63 (A031831), 64 (A031832), 65 (A031833), 66 (A031834), 67 (A031835), 68 (A031836), 69 (A031837), 70 (A031838), 71 (A031839), 72 (A031840), 73 (A031841), 74 (A031842), 75 (A031843), 76 (A031844), 77 (A031845), 78 (A031846), 79 (A031847), 80 (A031848), 81 (A031849), 82 (A031850), 83 (A031851), 84 (A031852), 85 (A031853), 86 (A031854), 87 (A031855), 88 (A031856), 89 (A031857), 90 (A031858), 91 (A031859), 92 (A031860), 93 (A031861), 94 (A031862), 95 (A031863), 96 (A031864), 97 (A031865), 98 (A031866), 99 (A031867), 100 (A031868)

Period of continued fraction for sqrt(k) contains at least m 1's

m = 2 (A013651), 3 (A013650)

Least term in period of continued fraction for sqrt(k) is m

m = 1 (A031425), 2 (A031426), 3 (A031427), 4 (A031428), 5 (A031429), 6 (A031430), 7 (A031431), 8 (A031432), 9 (A031433), 10 (A031434), 11 (A031689), 12 (A031690), 13 (A031691), 14 (A031692), 15 (A031693), 16 (A031694), 17 (A031695), 18 (A031696), 19 (A031697), 20 (A031698), 21 (A031699), 22 (A031700), 23 (A031701), 24 (A031702), 25 (A031703), 26 (A031704), 27 (A031705), 28 (A031706), 29 (A031707), 30 (A031708), 31 (A031709), 32 (A031710), 33 (A031711), 34 (A031712), 35 (A031713), 36 (A031714), 37 (A031715), 38 (A031716), 39 (A031717), 40 (A031718), 41 (A031719), 42 (A031720), 43 (A031721), 44 (A031722), 45 (A031723), 46 (A031724), 47 (A031725), 48 (A031726), 49 (A031727), 50 (A031728), 51 (A031729), 52 (A031730), 53 (A031731), 54 (A031732), 55 (A031733), 56 (A031734), 57 (A031735), 58 (A031736), 59 (A031737), 60 (A031738), 61 (A031739), 62 (A031740), 63 (A031741), 64 (A031742), 65 (A031743), 66 (A031744), 67 (A031745), 68 (A031746), 69 (A031747), 70 (A031748), 71 (A031749), 72 (A031750), 73 (A031751), 74 (A031752), 75 (A031753), 76 (A031754), 77 (A031755), 78 (A031756), 79 (A031757), 80 (A031758), 81 (A031759), 82 (A031760), 83 (A031761), 84 (A031762), 85 (A031763), 86 (A031764), 87 (A031765), 88 (A031766), 89 (A031767), 90 (A031768), 91 (A031769), 92 (A031770), 93 (A031771), 94 (A031772), 95 (A031773), 96 (A031774), 97 (A031775), 98 (A031776), 99 (A031777), 100 (A031778)

Numbers k such that continued fraction for sqrt(k) has period length m

m = 2 (A013642), 3 (A013643), 4 (A013644), 5 (A010337), 6 (A020347), 7 (A010338), 8 (A020348), 9 (A010339), 10 (A020349), 11 (A020350), 12 (A020351), 13 (A020352), 14 (A020353), 15 (A020354), 16 (A020355), 17 (A020356), 18 (A020357), 19 (A020358), 20 (A020359), 21 (A020360), 22 (A020361), 23 (A020362), 24 (A020363), 25 (A020364), 26 (A020365), 27 (A020366), 28 (A020367), 29 (A020368), 30 (A020369), 31 (A020370), 32 (A020371), 33 (A020372), 34 (A020373), 35 (A020374), 36 (A020375), 37 (A020376), 38 (A020377), 39 (A020378), 40 (A020379), 41 (A020380), 42 (A020381), 43 (A020382), 44 (A020383), 45 (A020384), 46 (A020385), 47 (A020386), 48 (A020387), 49 (A020388), 50 (A020389), 51 (A020390), 52 (A020391), 53 (A020392), 54 (A020393), 55 (A020394), 56 (A020395), 57 (A020396), 58 (A020397), 59 (A020398), 60 (A020399), 61 (A020400), 62 (A020401), 63 (A020402), 64 (A020403), 65 (A020404), 66 (A020405), 67 (A020406), 68 (A020407), 69 (A020408), 70 (A020409), 71 (A020410), 72 (A020411), 73 (A020412), 74 (A020413), 75 (A020414), 76 (A020415), 77 (A020416), 78 (A020417), 79 (A020418), 80 (A020419), 81 (A020420), 82 (A020421), 83 (A020422), 84 (A020423), 85 (A020424), 86 (A020425), 87 (A020426), 88 (A020427), 89 (A020428), 90 (A020429), 91 (A020430), 92 (A020431), 93 (A020432), 94 (A020433), 95 (A020434), 96 (A020435), 97 (A020436), 98 (A020437), 99 (A020438), 100 (A020439)

Numbers k such that continued fraction for sqrt(k) has even period and central term m

m = 1 (A031404), 2 (A031405), 3 (A031406), 4 (A031407), 5 (A031408), 6 (A031409), 7 (A031410), 8 (A031411), 9 (A031412), 10 (A031413), 11 (A031509), 12 (A031510), 13 (A031511), 14 (A031512), 15 (A031513), 16 (A031514), 17 (A031515), 18 (A031516), 19 (A031517), 20 (A031518), 21 (A031519), 22 (A031520), 23 (A031521), 24 (A031522), 25 (A031523), 26 (A031524), 27 (A031525), 28 (A031526), 29 (A031527), 30 (A031528), 31 (A031529), 32 (A031530), 33 (A031531), 34 (A031532), 35 (A031533), 36 (A031534), 37 (A031535), 38 (A031536), 39 (A031537), 40 (A031538), 41 (A031539), 42 (A031540), 43 (A031541), 44 (A031542), 45 (A031543), 46 (A031544), 47 (A031545), 48 (A031546), 49 (A031547), 50 (A031548), 51 (A031549), 52 (A031550), 53 (A031551), 54 (A031552), 55 (A031553), 56 (A031554), 57 (A031555), 58 (A031556), 59 (A031557), 60 (A031558), 61 (A031559), 62 (A031560), 63 (A031561), 64 (A031562), 65 (A031563), 66 (A031564), 67 (A031565), 68 (A031566), 69 (A031567), 70 (A031568), 71 (A031569), 72 (A031570), 73 (A031571), 74 (A031572), 75 (A031573), 76 (A031574), 77 (A031575), 78 (A031576), 79 (A031577), 80 (A031578), 81 (A031579), 82 (A031580), 83 (A031581), 84 (A031582), 85 (A031583), 86 (A031584), 87 (A031585), 88 (A031586), 89 (A031587), 90 (A031588), 91 (A031589), 92 (A031590), 93 (A031591), 94 (A031592), 95 (A031593), 96 (A031594), 97 (A031595), 98 (A031596), 99 (A031597), 100 (A031598)

Numbers k such that continued fraction for sqrt(k) has odd period and central term m

m = 1 (A031414), 2 (A031415), 3 (A031416), 4 (A031417), 5 (A031418), 6 (A031419), 7 (A031420), 8 (A031421), 9 (A031422), 10 (A031423), 11 (A031599), 12 (A031600), 13 (A031601), 14 (A031602), 15 (A031603), 16 (A031604), 17 (A031605), 18 (A031606), 19 (A031607), 20 (A031608), 21 (A031609), 22 (A031610), 23 (A031611), 24 (A031612), 25 (A031613), 26 (A031614), 27 (A031615), 28 (A031616), 29 (A031617), 30 (A031618), 31 (A031619), 32 (A031620), 33 (A031621), 34 (A031622), 35 (A031623), 36 (A031624), 37 (A031625), 38 (A031626), 39 (A031627), 40 (A031628), 41 (A031629), 42 (A031630), 43 (A031631), 44 (A031632), 45 (A031633), 46 (A031634), 47 (A031635), 48 (A031636), 49 (A031637), 50 (A031638), 51 (A031639), 52 (A031640), 53 (A031641), 54 (A031642), 55 (A031643), 56 (A031644), 57 (A031645), 58 (A031646), 59 (A031647), 60 (A031648), 61 (A031649), 62 (A031650), 63 (A031651), 64 (A031652), 65 (A031653), 66 (A031654), 67 (A031655), 68 (A031656), 69 (A031657), 70 (A031658), 71 (A031659), 72 (A031660), 73 (A031661), 74 (A031662), 75 (A031663), 76 (A031664), 77 (A031665), 78 (A031666), 79 (A031667), 80 (A031668), 81 (A031669), 82 (A031670), 83 (A031671), 84 (A031672), 85 (A031673), 86 (A031674), 87 (A031675), 88 (A031676), 89 (A031677), 90 (A031678), 91 (A031679), 92 (A031680), 93 (A031681), 94 (A031682), 95 (A031683), 96 (A031684), 97 (A031685), 98 (A031686), 99 (A031687), 100 (A031688)

Period length of continued fraction for sqrt(m)*n

m = 2 (A064848), 3 (A064849), 5 (A064850), 6 (A064851), 7 (A064860), 10 (A064862), 11 (A064863), 13 (A064864), 14 (A064887), 15 (A064897), 17 (A064912), 19 (A064913), 21 (A064925), 22 (A064926), 23 (A064927)