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A071135 Squares which repeat with at least two full periods when written in base 9. 9
557904400, 1255284900, 2231617600, 508239242281, 110723679691024, 267200559990920521, 4624943568803015273104, 89426738951269414045129, 106343953870710063227329, 141828621071731373745001, 153228095100765507880225, 155946118585671902125225 (list; graph; refs; listen; history; text; internal format)
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: A214480 A251441 A234199 * A303268 A186961 A032755

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

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Last modified August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)