

A031551


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 53.


2



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
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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
Includes 2809 * k^2 + 2 * k for k >= 1, where the continued fraction has initial term 53*k and periodic part [53, 106*k], and 3025 * k^2  2 * k for k >= 1, where the continued fraction has initial term 55*k1 and periodic part [1, 53, 1, 110*k2].  Robert Israel, Apr 11 2023


LINKS



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



