A031521 Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 23.

531, 547, 563, 571, 587, 599, 603, 607, 619, 623, 2120, 2144, 2152, 2176, 2216, 2240, 2344, 2368, 2432, 2440, 2496, 4767, 4839, 4911, 4983, 5055, 5127, 5199, 5271, 5487, 5547, 5619, 8472, 8664, 8728, 8856, 8984, 9112, 9304, 9352, 9368, 9432, 9496, 9624

Offset

1,1

Comments

The "central term" is the term that appears at 1/2 the length of the period of the continued fraction. - Harvey P. Dale, Feb 25 2012

Links

Table of n, a(n) for n=1..44.

Mathematica

cf2Q[n_]:=Module[{cf=ContinuedFraction[Sqrt[n]], len}, If[Length[cf]==1, len=1, len=Length[cf[[2]]]]; EvenQ[len]&&cf[[2, len/2]]==23]; Select[ Range[10000], cf2Q](* Harvey P. Dale, Feb 26 2012 *)

Crossrefs

Sequence in context: A174761 A031967 A345387 * A156772 A031701 A158367

Adjacent sequences: A031518 A031519 A031520 * A031522 A031523 A031524

Keyword

nonn

Author

David W. Wilson

Extensions

Definition edited by Harvey P. Dale, Jun 08 2023

Status

approved