A031573 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 75.

5627, 5639, 5643, 5647, 5651, 5659, 5667, 5683, 5711, 5723, 5731, 5739, 5743, 5763, 5767, 5779, 5783, 5787, 5791, 5807, 5827, 5831, 5839, 5843, 5851, 5867, 5879, 5891, 5899, 5903, 5923, 5927, 22504, 22528, 22624, 22656, 22688, 22696, 22720, 22784

Offset

1,1

Comments

The "central term" is at period/2, not at period/2 + 1. - Harvey P. Dale, Feb 20 2013

Links

Table of n, a(n) for n=1..40.

Mathematica

epQ[n_]:=Module[{srt=Sqrt[n], cf, len}, cf=If[IntegerQ[srt], {1}, ContinuedFraction[ srt] [[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]]==75]; Select[Range[ 23000], epQ] (* Harvey P. Dale, Feb 20 2013 *)

Crossrefs

Sequence in context: A247261 A203831 A014799 * A031753 A045128 A229591

Adjacent sequences: A031570 A031571 A031572 * A031574 A031575 A031576

Keyword

nonn

Author

David W. Wilson

Extensions

Definition corrected by Harvey P. Dale, Sep 04 2023

Status

approved