A071135 Squares which repeat with at least two full periods when written in base 9.

557904400, 1255284900, 2231617600, 508239242281, 110723679691024, 267200559990920521, 4624943568803015273104, 89426738951269414045129, 106343953870710063227329, 141828621071731373745001, 153228095100765507880225, 155946118585671902125225

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..15 (terms < 9^25)

Example

23620^2 = 557904400 = 13857|13857 in base 9.
712909^2 = 508239242281 = 171676|171676|1 in base 9.

Mathematica

psq[b_, nd_] := Block[{sq={}, r, x}, Do[r = Mod[nd, p]; Do[x = (b^( Floor[nd/p] p) - 1)/(b^p - 1) t  b^r + Floor[t/b^(p - r)]; If[ IntegerQ@ Sqrt@ x, AppendTo[ sq, x]], {t, b^(p - 1), b^p - 1}], {p, nd/2}]; sq]; Union @@ (psq[9, #] & /@ Range[10]) (* Giovanni Resta, Aug 01 2018 *)

Crossrefs

Cf. A071128 (base 2) - A071134 (base 8), A069919 (base 10).

Sequence in context: A251441 A350136 A234199 * A335561 A303268 A186961

Adjacent sequences: A071132 A071133 A071134 * A071136 A071137 A071138

Keyword

base,nonn

Author

Erich Friedman, May 28 2002

Extensions

a(5)-a(12) from Giovanni Resta, Aug 01 2018

Status

approved