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A031551 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 53. 1
2811, 2819, 2839, 2843, 2851, 2859, 2863, 2879, 2887, 2903, 2911, 2927, 2931, 2939, 2963, 2971, 2979, 2999, 3007, 3011, 3019, 3023, 11240, 11264, 11296, 11328, 11336, 11424, 11432, 11456, 11520, 11560, 11584, 11616, 11624, 11648, 11680, 11712, 11720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

"Central term" means the term at 1/2 of the length of the repeating part, not the term following that term, e.g., if the terms are {a,b,c,d}, the "central term" is b, not c. - Harvey P. Dale, May 19 2012

LINKS

Table of n, a(n) for n=1..39.

MATHEMATICA

epQ[n_]:=Module[{p=ContinuedFraction[Sqrt[n]][[2]], len}, len=Length[p]; EvenQ[len]&&p[[len/2]]==53]; nn=12000; With[{trms=Complement[Range[ nn], Range[Floor[Sqrt[nn]]]^2]}, Select[trms, epQ]]  (* Harvey P. Dale, May 19 2012 *)

CROSSREFS

Sequence in context: A306849 A022233 A102170 * A031731 A252048 A254254

Adjacent sequences:  A031548 A031549 A031550 * A031552 A031553 A031554

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 23 16:20 EDT 2021. Contains 348215 sequences. (Running on oeis4.)