A031630 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 42.

11261, 21953, 22549, 36181, 36562, 37330, 53945, 54877, 55817, 132058, 165197, 166825, 199357, 235754, 238673, 240629, 242593, 243578, 277301, 283649, 284714, 285781, 287921, 337129, 372941, 377837, 426065, 427370, 428677, 431297

Offset

1,1

Links

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

Mathematica

cf42Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 2}, ContinuedFraction[s][[2]]]; len= Length[ cf]; OddQ[len]&&cf[[Floor[len/2]]]==cf[[Ceiling[len/2]]]==42]; Select[Range[ 450000], cf42Q] (* Harvey P. Dale, Aug 10 2023 *)

Crossrefs

Sequence in context: A104316 A237171 A246248 * A064870 A051520 A051346

Adjacent sequences: A031627 A031628 A031629 * A031631 A031632 A031633

Keyword

nonn

Author

David W. Wilson

Extensions

First term 1765 removed by Georg Fischer, Jun 16 2019

Status

approved