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%I #5 Aug 01 2018 10:28:39
%S 16,400,900,1600,29584,70627216,394618225,2214643600,4982948100,
%T 8858574400,16052636601,64210546404,169556179984,727092173809,
%U 1120597967889,2908368695236,6543829564281,6703226505481,79822717134736,407103419654416,12766762698010000
%N Squares which repeat with at least two full periods when written in base 7.
%H Giovanni Resta, <a href="/A071133/b071133.txt">Table of n, a(n) for n = 1..39</a> (terms < 7^29)
%e 19865^2 = 394618225 = 12531|12531|1 in base 7.
%e 411772^2 = 169556179984 = 1515152|1515152 in base 7.
%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[7, #] & /@ Range[12]) (* _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 a(17)-a(21) from _Giovanni Resta_, Aug 01 2018
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