A031526 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 28.

786, 802, 822, 834, 838, 862, 866, 878, 886, 898, 1767, 1797, 1803, 1812, 1821, 1833, 1839, 1857, 1884, 1893, 1911, 1929, 1941, 1956, 1977, 1983, 2013, 2022, 3140, 3148, 3180, 3188, 3196, 3212, 3228, 3236, 3244, 3260, 3276, 3284, 3292, 3308, 3316, 3340

Offset

1,1

Links

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

Mathematica

okQ[n_] := Module[{cf, p}, cf = ContinuedFraction[Sqrt[n]]; p = FindTransientRepeat[cf, 2][[1, 2]]; EvenQ[lp = Length[p]] && p[[lp/2]] == 28];
Reap[Do[If[okQ[n], Sow[n]], {n, 1, 3340}]][[2, 1]] // Quiet (* Jean-François Alcover, Dec 14 2017 *)
cf28Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 28]; Select[ Range[3400], cf28Q] (* Harvey P. Dale, Jun 03 2021 *)

Crossrefs

Sequence in context: A159896 A031734 A097776 * A108795 A097774 A031896

Adjacent sequences: A031523 A031524 A031525 * A031527 A031528 A031529

Keyword

nonn

Author

David W. Wilson

Status

approved