A069919 Squares which repeat with at least two full periods when written in base 10.

69696, 56722567225, 95540955409, 1108033241108033241, 1220096161220096161, 4312080784312080784, 4432132964432132964, 4880384644880384644, 9024307889024307889, 9972299169972299169, 225607697225607697225, 946308825294630882529, 1322314049613223140496

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..21 (terms < 10^24)

Example

264^2 = 69|69|6 in base 10.
15020242915^2 = 225607697|225607697|225 in base 10.
36363636364^2 = 13223140496|13223140496 in base 10.

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[10, #] & /@ Range[11]) (* Giovanni Resta, Aug 01 2018 *)

Crossrefs

Cf. A071128 (base 2) - A071135 (base 9), A116502.

Sequence in context: A224324 A053075 A154818 * A116502 A190934 A043600

Adjacent sequences: A069916 A069917 A069918 * A069920 A069921 A069922

Keyword

base,nonn

Author

Erich Friedman, Apr 25 2002

Extensions

Corrected and extended by Jason Earls, Jun 16 2002

Data corrected and extended by Giovanni Resta, Aug 01 2018

Status

approved