A071131 Squares which repeat with at least two full periods when written in base 5.

7056, 71824, 17380561, 10479821641, 1695422743056, 3046710023334121, 3484661204178361, 4238552821180561, 16390460540754756, 2341118082098985289, 49597060188790044841, 413921144300672743056, 931719854156507158681, 1149780956458574459881, 1254278391764733006841

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..23 (terms < 5^33)

Example

268^2 = 71824 = 424|424|4 in base 5.
1302084^2 = 1695422743056 = 210234211|210234211 in base 5.

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[5, #] & /@ Range[15]) (* Giovanni Resta, Aug 01 2018 *)

Crossrefs

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

Sequence in context: A116332 A234545 A250850 * A238520 A230975 A031582

Adjacent sequences: A071128 A071129 A071130 * A071132 A071133 A071134

Keyword

base,nonn

Author

Erich Friedman, May 28 2002

Extensions

a(5)-a(15) from Giovanni Resta, Aug 01 2018

Status

approved