A071132 - OEIS

%I #5 Aug 01 2018 10:28:33

%S 5776,190096,6739216,97990201,241989136,242611776,3975176401,

%T 8707875856,8711608896,14393520729,25588481296,39982002025,

%U 57574082916,95174101009,149392299169,313461135376,313483530816,380696404036,4724628251641,11284466503696,11284600873536

%N Squares which repeat with at least two full periods when written in base 6.

%H Giovanni Resta, <a href="/A071132/b071132.txt">Table of n, a(n) for n = 1..54</a> (terms < 6^29)

%e 76^2 = 5776 = 42|42|4 in base 6.

%e 119973^2 = 14393520729 = 1034013|1034013 in base 6.

%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[6, #] & /@ Range[13]) (* _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(12), a(13), a(16) and more terms from _Giovanni Resta_, Aug 01 2018