A071135 Squares which repeat with at least two full periods when written in base 9.
557904400, 1255284900, 2231617600, 508239242281, 110723679691024, 267200559990920521, 4624943568803015273104, 89426738951269414045129, 106343953870710063227329, 141828621071731373745001, 153228095100765507880225, 155946118585671902125225
Offset: 1
Examples
23620^2 = 557904400 = 13857|13857 in base 9. 712909^2 = 508239242281 = 171676|171676|1 in base 9.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..15 (terms < 9^25)
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[9, #] & /@ Range[10]) (* Giovanni Resta, Aug 01 2018 *)
Extensions
a(5)-a(12) from Giovanni Resta, Aug 01 2018