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 A306972 Nonsquare numbers n such that the difference between sqrt(n) and its best rational approximation as x/y with y<=n produces a new minimum of abs(sqrt(n)-x/y). x/y is provided as A306973/A306974. 3
 2, 3, 5, 8, 10, 15, 17, 19, 20, 21, 28, 44, 68, 72, 90, 107, 114, 115, 156, 159, 164, 267, 278, 294, 336, 427, 455, 464, 592, 644, 665, 754, 998, 1040, 1139, 1173, 1278, 1314, 1335, 1463, 1503, 1593, 1943, 2175, 2262, 2520, 2642, 2873, 2978, 3003, 3047, 3181, 3197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE k s=sqrt(k)     x/y  |s - x/y|    2 1.4142135...  3/2  0.0857864... new minimum    3 1.7320508...  5/3  0.0653841... new minimum    5 2.2360679...  9/4  0.0139320... new minimum    6 2.4494897...  5/2  0.0505102...    7 2.6457513...  8/3  0.0209153...    8 2.8284271... 17/6  0.0049062... new minimum   10 3.1622776... 19/6  0.0043890... new minimum   11 3.3166247... 10/3  0.0167085...   12 3.4641016...  7/2  0.0358983...   13 3.6055512... 18/5  0.0055512...   14 3.7416573... 15/4  0.0083426...   15 3.8729833... 31/8  0.0020166... new minimum   17 4.1231056... 33/8  0.0018943... new minimum   18 4.2426406... 17/4  0.0073593...   19 4.3588989... 61/14 0.0017560... new minimum   20 4.4721359... 76/17 0.0015477... new minimum .   a(1)..a(9)    = [2, 3, 5,  8, 10, 15, 17, 19, 20]   A306973(1..9) = [3, 5, 9, 17, 19, 31, 33, 61, 76]   A306974(1..9) = [2, 3, 4,  6,  6,  8,  8, 14, 17] PROG (PARI) dmin=1; for(k=2, 3200, if(!issquare(k), s=sqrt(k); d=abs(s-bestappr(s, k)); if(d

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Last modified April 13 00:24 EDT 2021. Contains 342934 sequences. (Running on oeis4.)