This site is supported by donations to The OEIS Foundation.
User:Georg Fischer/Concatenated numbers
From OeisWiki
This index lists 100 similiar sequences in the range A115426 - A116224 with names like:
Numbers n such that the concatenation of n with n+i gives a square. Numbers n such that n concatenated with n+i gives the product of two numbers which differ by j. Numbers n such that n concatenated with itself gives the product of two numbers which differ by j.
In the following, we use //
for the concatenation of the decimal digits of n and n+i, we set i=0 for "with itself" and j=0 for "gives a square", and we write the required equality with a common formula:
n // n+i = m * (m+j)
Examples (from A116133)
i = -4, j = 9: 8776//8772 = 9364 * 9373 or i = +4. j = 7: 8776//8780 = 9365 * 9372
Index (ascending sequence numbers)
A115426 n // n+2 = m * (m+0) 7874,8119,69476962,98010199,108746354942,4492121103... A115428 n // n+5 = m * (m+0) 1,4,20,31,14564,38239,69919,120395,426436,902596,74... A115429 n // n+8 = m * (m+0) 6001,6433,11085116,44496481,96040393,115916930617,2... A115430 n // n+9 = m * (m+0) 216,287,515,675,1175,4320,82640,960795,1322312,4049... A115431 n // n-2 = m * (m+0) 6,5346,8083,10578,45531,58626,2392902,2609443,72728... A115432 n // n-4 = m * (m+0) 65,6653,9605,218413,283720,996005,58446925,99960005... A115433 n // n-5 = m * (m+0) 21,30,902406,959721,6040059046,6242406405,984241000... A115434 n // n-7 = m * (m+0) 8,16,1337032,2084503,2953232,4023943,13300336130701... A115435 n // n-8 = m * (m+0) 2137,2892,6369,12217,21964,28233,42312,4978977,9571... A115436 n // n-9 = m * (m+0) 50,5234,9410,638370,994010,12477933,41829698,999400... A115437 n // n+4 = m * (m+0) 96,205,300,477,732,1920,3157,52896,120085,427020,82... A116094 n // n-9 = m * (m+1) 15,771,939,2099721,2935179,5235841,5424812334857206... A116095 n // n-9 = m * (m+2) 2137,2892,6369,12217,21964,28233,42312,4978977,9571... A116096 n // n-9 = m * (m+4) 21,30,902406,959721,6040059046,6242406405,984241000... A116097 n // n-9 = m * (m+5) 92185,1453156572932210152879253333913,3829098407015... A116098 n // n-9 = m * (m+6) 11,101,1001,10001,100001,1000001,10000001,100000001... A116099 n // n-9 = m * (m+7) 69,59898667,79493157,13412927190959690154913903,141... A116101 n // n-8 = m * (m+1) 40,54999166056446260156057520,579754639429451550431... A116102 n // n-8 = m * (m+2) 16,1337032,2084503,2953232,4023943,1330033613070195... A116103 n // n-8 = m * (m+3) 58,1552909498221642960203840517299022287877411846,1... A116104 n // n-8 = m * (m+4) 65,6653,9605,218413,283720,996005,58446925,99960005... A116105 n // n-8 = m * (m+5) 5303944,6677714,2070936216988528558,296942817273887... A116106 n // n-8 = m * (m+6) 9,13,99,103,183,328,528,715,999,1003,6099,9999,1000... A116107 n // n-8 = m * (m+7) 52,63716866,48793687600063875363014809897052,600207... A116109 n // n-8 = m * (m+9) 94,210,294,994,5880,9994,52888,99994,127044,414180,... A116110 n // n-7 = m * (m+3) 55,5255,6295,75511,92137,5551405,7943911,1257669432... A116112 n // n-7 = m * (m+7) 17,35,10408517,45884051,62918301,111629052264583831... A116113 n // n-7 = m * (m+8) 95,216,287,515,675,995,1175,4320,9995,82640,99995,9... A116114 n // n-7 = m * (m+9) 13,493,607,629,757,17927,33247,93869,19467217,31223... A116115 n // n-6 = m * (m+1) 58,1552909498221642960203840517299022287877411846,1... A116116 n // n-6 = m * (m+2) 21,30,902406,959721,6040059046,6242406405,984241000... A116117 n // n-6 = m * (m+4) 5346,8083,10578,45531,58626,2392902,2609443,7272838... A116118 n // n-6 = m * (m+5) 10,12,100,102,132,406,510,852,1000,1002,7930,10000,... A116119 n // n-6 = m * (m+7) 96,150,186,324,376,666,996,2046,3000,9996,82650,999... A116120 n // n-5 = m * (m+1) 7,55,5255,6295,75511,92137,5551405,7943911,12576694... A116121 n // n-5 = m * (m+2) 65,6653,9605,218413,283720,996005,58446925,99960005... A116122 n // n-5 = m * (m+3) 92185,1453156572932210152879253333913,3829098407015... A116123 n // n-5 = m * (m+4) 82,8242,9802,538277,998002,77837026,99980002,792254... A116124 n // n-5 = m * (m+5) 61,65479,84289,106609,225649,275599,453589,1869505,... A116125 n // n-5 = m * (m+6) 7,97,205,300,477,732,997,1920,3157,9997,52896,99997... A116126 n // n-5 = m * (m+8) 10,6752089,6448802889351008245,18894512461523256139... A116128 n // n-4 = m * (m+3) 5303944,6677714,2070936216988528558,296942817273887... A116129 n // n-4 = m * (m+4) 11,101,1001,10001,100001,1000001,10000001,100000001... A116130 n // n-4 = m * (m+5) 8,98,590,738,830,998,1080,4508,9998,20660,29754,999... A116131 n // n-4 = m * (m+6) 20,31,14564,38239,69919,120395,426436,902596,747802... A116132 n // n-4 = m * (m+7) 74,59264,510782,906902,81790664,92776472,1087685604... A116133 n // n-4 = m * (m+9) 64,1876,3214,8776,17227120144584448354,193910879904... A116134 n // n-3 = m * (m+1) 92185,1453156572932210152879253333913,3829098407015... A116135 n // n-3 = m * (m+2) 6,5346,8083,10578,45531,58626,2392902,2609443,72728... A116136 n // n-3 = m * (m+4) 9,99,183,328,528,715,999,6099,9999,13224,40495,9999... A116139 n // n-3 = m * (m+8) 43,20440836,30017751,61336887,524008711977553344261... A116140 n // n-3 = m * (m+9) 5,7403,8885,12563,41675,54239,2353623,2650793,77175... A116141 n // n-2 = m * (m+1) 4,5303944,6677714,2070936216988528558,2969428172738... A116143 n // n-2 = m * (m+3) 10,100,132,406,510,852,1000,7930,10000,66942,100000... A116146 n // n-2 = m * (m+8) 47,550,802,570035,623387,1327222,4041011,8252210,16... A116147 n // n-2 = m * (m+9) 4962,237412345332,262912791034,468307643502,... A116152 n // n-1 = m * (m+7) 9,11,45,18281,32769,56891,180689,330539,959481,1850... A116153 n // n-1 = m * (m+9) 13,41,653,2287,2723,5491,23240971,26823191,60249661... A116154 n // n+0 = m * (m+1) 132,406,510,852,7930,66942,113322,440056,5289256,58... A116158 n // n+0 = m * (m+5) 6,96,150,186,324,376,666,996,2046,3000,9996,82650,9... A116159 n // n+0 = m * (m+6) 5,95,216,287,515,675,995,1175,4320,9995,82640,99995... A116160 n // n+0 = m * (m+7) 4,94,210,294,994,5880,9994,52888,99994,127044,41418... A116161 n // n+0 = m * (m+8) 3,93,145,384,505,820,993,7680,9993,20665,29748,9999... A116162 n // n+0 = m * (m+9) 2,92,180,332,486,536,992,9720,9992,13220,40502,9999... A116167 n // n+1 = m * (m+7) 7,493,607,629,757,17927,33247,93869,19467217,312238... A116168 n // n+1 = m * (m+8) 19,32,16284704,35576083,157648361879960242601196397... A116169 n // n+1 = m * (m+9) 9,49,1166975893986638437392162264780939,14111742682... A116170 n // n+2 = m * (m+1) 590,738,830,1080,4508,20660,29754,980300,6694218,49... A116171 n // n+2 = m * (m+3) 8,52,63716866,48793687600063875363014809897052,6002... A116172 n // n+2 = m * (m+5) 2,74,59264,510782,906902,81790664,92776472,10876856... A116173 n // n+2 = m * (m+6) 6752089,6448802889351008245,18894512461523256139943... A116174 n // n+2 = m * (m+8) 1143,4382,4943,24941511,25058558,94090583,616729341... A116175 n // n+2 = m * (m+9) 1122070,1538990,3692998,4422608,1661985831086046580... A116177 n // n+3 = m * (m+2) 205,300,477,732,1920,3157,52896,120085,427020,82644... A116179 n // n+3 = m * (m+5) 1,3,81,1353,3997,7723,23761,26271,76771,1415683,389... A116180 n // n+3 = m * (m+7) 7137,7767,47783068991048776635,48797525371338932241... A116181 n // n+3 = m * (m+8) 57,1062,4545,9517,650408168237059191482745572128245... A116182 n // n+3 = m * (m+9) 3,14879,37733,78677,1358679,3986627,5217267,7109758... A116185 n // n+4 = m * (m+3) 150,186,324,376,666,2046,3000,82650,100384,466716,1... A116187 n // n+4 = m * (m+6) 12,43,20440836,30017751,61336887,524008711977553344... A116189 n // n+4 = m * (m+8) 4,80,10736,45205,58256,481580,810181,5321861,822382... A116190 n // n+4 = m * (m+9) 16,36,12366,42036,64996,1589736168,1921234732,31548... A116193 n // n+5 = m * (m+5) 11,45,18281,32769,56891,180689,330539,959481,185020... A116194 n // n+5 = m * (m+6) 1,2,10,47,550,802,570035,623387,1327222,4041011,825... A116195 n // n+5 = m * (m+7) 7403,8885,12563,41675,54239,2353623,2650793,7717533... A116196 n // n+5 = m * (m+8) 68,12585135,17104748,34388975,41634068,110078841938... A116197 n // n+5 = m * (m+9) 25,2448207281,2552334847,9492271895,107130247755970... A116200 n // n+6 = m * (m+5) 210,294,5880,52888,127044,414180,8264470,12456750,4... A116202 n // n+6 = m * (m+8) 7,54,234,267,894,58227,7962242238271227055830015496... A116203 n // n+6 = m * (m+9) 24,26,1014,1196,4280,4646,10512559797957763880,2211... A116205 n // n+7 = m * (m+3) 1,81,1353,3997,7723,23761,26271,76771,1415683,38905... A116207 n // n+7 = m * (m+5) 493,607,629,757,17927,33247,93869,19467217,31223879... A116208 n // n+7 = m * (m+6) 145,384,505,820,7680,20665,29748,480340,6694209,778... A116209 n // n+7 = m * (m+7) 1,13,41,653,2287,2723,5491,23240971,26823191,602496... A116210 n // n+7 = m * (m+8) 73,101,466,577,913,938,1027699544347561123497066503... A116211 n // n+7 = m * (m+9) 1953,3115,6153,1016574047215119910181525023,2440558... A116215 n // n+8 = m * (m+7) 92,180,332,486,536,9720,13220,40502,941486,2066120,... A116216 n // n+8 = m * (m+9) 122,424,694,778,878,11012,17872,33322,44644,1001276... A116223 n // n+9 = m * (m+8) 136,399,600,744,8184,66951,134199,401536,5289264,12... A116224 n // n+9 = m * (m+9) 23,27,10357253,10577583,45531191,45991881,128238416...
Candidates for duplicates
A116098 n // n-9 = m * (m+6) 11,101,1001,10001,100001,1000001,10000001,100000001... A116129 n // n-4 = m * (m+4) 11,101,1001,10001,100001,1000001,10000001,100000001... ---- A115433 n // n-5 = m * (m+0) 21,30,902406,959721,6040059046,6242406405,984241000... A116096 n // n-9 = m * (m+4) 21,30,902406,959721,6040059046,6242406405,984241000... A116116 n // n-6 = m * (m+2) 21,30,902406,959721,6040059046,6242406405,984241000... ---- A115435 n // n-8 = m * (m+0) 2137,2892,6369,12217,21964,28233,42312,4978977,9571... A116095 n // n-9 = m * (m+2) 2137,2892,6369,12217,21964,28233,42312,4978977,9571... ---- A116141 n // n-2 = m * (m+1) 4,5303944,6677714,2070936216988528558,2969428172738... A116105 n // n-8 = m * (m+5) 5303944,6677714,2070936216988528558,296942817273887... A116128 n // n-4 = m * (m+3) 5303944,6677714,2070936216988528558,296942817273887... ---- A116103 n // n-8 = m * (m+3) 58,1552909498221642960203840517299022287877411846,1... A116115 n // n-6 = m * (m+1) 58,1552909498221642960203840517299022287877411846,1... ---- A115431 n // n-2 = m * (m+0) 6,5346,8083,10578,45531,58626,2392902,2609443,72728... A116135 n // n-3 = m * (m+2) 6,5346,8083,10578,45531,58626,2392902,2609443,72728... ---- A115432 n // n-4 = m * (m+0) 65,6653,9605,218413,283720,996005,58446925,99960005... A116104 n // n-8 = m * (m+4) 65,6653,9605,218413,283720,996005,58446925,99960005... A116121 n // n-5 = m * (m+2) 65,6653,9605,218413,283720,996005,58446925,99960005... ---- A116097 n // n-9 = m * (m+5) 92185,1453156572932210152879253333913,3829098407015... A116122 n // n-5 = m * (m+3) 92185,1453156572932210152879253333913,3829098407015... A116134 n // n-3 = m * (m+1) 92185,1453156572932210152879253333913,3829098407015...