A031520 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 22.

486, 498, 502, 514, 526, 534, 542, 562, 566, 574, 1092, 1101, 1119, 1137, 1149, 1191, 1209, 1236, 1257, 1263, 1281, 1293, 1940, 1948, 1964, 1972, 1996, 2012, 2036, 2044, 2060, 2076, 2084, 2092, 2108, 2124, 2132, 2140, 2156, 2164, 2188, 2204, 2220, 2228

Offset

1,1

Links

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

Mathematica

cf22Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 22]; Select[Range[2300], cf22Q] (* Harvey P. Dale, Jul 07 2020 *)

Crossrefs

Sequence in context: A156774 A031632 A097767 * A235525 A249227 A130181

Adjacent sequences: A031517 A031518 A031519 * A031521 A031522 A031523

Keyword

nonn

Author

David W. Wilson

Status

approved