A031645 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 57.

40049, 40853, 66130, 67162, 67681, 98717, 188581, 235514, 237458, 238433, 298477, 300665, 365257, 370105, 436129, 440098, 442754, 508994, 510421, 513281, 514714, 516149, 521909, 523354, 524801, 593629, 686425, 703085, 785957, 796625

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Mathematica

cf57Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[s][[2]]]; len= Length[cf]; OddQ[len]&&cf[[(len-1)/2]]==cf[[(len+1)/2]]==57]; Select[Range[800000], cf57Q] (* Harvey P. Dale, Jan 17 2024 *)

Crossrefs

Sequence in context: A270261 A272889 A126104 * A250079 A237238 A389952

Adjacent sequences: A031642 A031643 A031644 * A031646 A031647 A031648

Keyword

nonn

Author

David W. Wilson

Extensions

First term 3250 removed by Georg Fischer, Jun 16 2019

Status

approved