A071128 Squares which repeat with at least two full periods when written in base 2.

36, 1849, 6241, 29929, 418609, 672400, 1320201, 7458361, 28121809, 119355625, 302794801, 386554921, 1211179204, 1277991001, 1967188609, 5111964004, 7681646025, 30542106169, 73073443041, 79698371481, 91424593225, 120297291921, 292293772164, 318793485924

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..106 (terms < 2^72)

Example

173^2 = 29929 = 1110100|1110100|1 in base 2.

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[2, #] & /@ Range[32]) (* Giovanni Resta, Aug 01 2018 *)

Crossrefs

Cf. A071129 (base 3) - A071135 (base 9), A069919 (base 10).

Sequence in context: A054980 A151640 A025754 * A065782 A374393 A160482

Adjacent sequences: A071125 A071126 A071127 * A071129 A071130 A071131

Keyword

base,nonn

Author

Erich Friedman, May 28 2002

Extensions

Missing a(13), a(17), and a(21) from Giovanni Resta, Aug 01 2018

Status

approved