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 A031509 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 11. 2
 123, 127, 131, 139, 151, 163, 167, 488, 512, 520, 544, 608, 640, 672, 1095, 1167, 1383, 1455, 1515, 1944, 2008, 2136, 2264, 2456, 2648, 2696, 3035, 3115, 3215, 3235, 3415, 3515, 3635, 3715, 3735, 3835, 3935, 4115, 4135, 4215, 4368, 4944, 5496, 5943, 5971 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..1000 EXAMPLE The c.f. expansion of sqrt(127) is 11, [3, 1, 2, 2, 7, 11, 7, 2, 2, 1, 3, 22], [3, 1, 2, 2, 7, 11, 7, 2, 2, 1, 3, 22], ... If the 22 is deleted from the periodic part the central term is 11. - N. J. A. Sloane, Aug 17 2021 MAPLE # Maple 2016 or later. filter:= proc(n) uses NumberTheory; local R;   if issqr(n) then return false fi;   R:= Term(ContinuedFraction(sqrt(n)), periodic)[2];   nops(R)::even and R[nops(R)/2] = 11 end proc: select(filter, [\$2..10000]); # Robert Israel, Jun 07 2019 MATHEMATICA okQ[k_] := Module[{c, lc}, If[IntegerQ[Sqrt[k]], False,      c = ContinuedFraction[Sqrt[k]]; lc = Length[c[[2]]];      EvenQ[lc] && c[[2, lc/2]] == 11]]; Select[Range[10000], okQ] (* Jean-François Alcover, Jul 09 2021 *) CROSSREFS Sequence in context: A192231 A341992 A077378 * A247616 A119426 A138059 Adjacent sequences:  A031506 A031507 A031508 * A031510 A031511 A031512 KEYWORD nonn AUTHOR EXTENSIONS Definitions of A031509-A031598 clarified by N. J. A. Sloane, Aug 17 2021 STATUS approved

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Last modified December 6 10:19 EST 2021. Contains 349563 sequences. (Running on oeis4.)