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%I #6 Aug 01 2018 10:28:50
%S 9,36,6241,116964,418609,28121809,477247716,1277991001,1967188609,
%T 5111964004,7681646025,73073443041,79698371481,91424593225,
%U 120297291921,292293772164,318793485924,1954689202404,5429696889241,5480313774049,21718787556964,21921255096196
%N Squares which repeat with at least two full periods when written in base 8.
%H Giovanni Resta, <a href="/A071134/b071134.txt">Table of n, a(n) for n = 1..57</a> (terms < 8^27)
%e 647^2 = 418609 = 146|146|1 in base 8.
%e 21846^2 = 477247716 = 34344|34344 in base 8.
%t 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[8, #] & /@ Range[11]) (* _Giovanni Resta_, Aug 01 2018 *)
%Y Cf. A071128 (base 2) - A071135 (base 9), A069919 (base 10).
%K base,nonn
%O 1,1
%A _Erich Friedman_, May 28 2002
%E Missing a(18) and more terms from _Giovanni Resta_, Aug 01 2018