A071133 Squares which repeat with at least two full periods when written in base 7.

16, 400, 900, 1600, 29584, 70627216, 394618225, 2214643600, 4982948100, 8858574400, 16052636601, 64210546404, 169556179984, 727092173809, 1120597967889, 2908368695236, 6543829564281, 6703226505481, 79822717134736, 407103419654416, 12766762698010000

Offset: 1

Author

Erich Friedman, May 28 2002

Keywords

• base
• nonn

Examples

			19865^2 = 394618225 = 12531|12531|1 in base 7.
411772^2 = 169556179984 = 1515152|1515152 in base 7.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..39 (terms < 7^29)

Crossrefs

Cf. A071128 (base 2) - A071135 (base 9), A069919 (base 10).

Programs

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[7, #] & /@ Range[12]) (* Giovanni Resta, Aug 01 2018 *)

Extensions

a(17)-a(21) from Giovanni Resta, Aug 01 2018