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A071131 Squares which repeat with at least two full periods when written in base 5. 1

%I

%S 7056,71824,17380561,10479821641,1695422743056,3046710023334121,

%T 3484661204178361,4238552821180561,16390460540754756,

%U 2341118082098985289,49597060188790044841,413921144300672743056,931719854156507158681,1149780956458574459881,1254278391764733006841

%N Squares which repeat with at least two full periods when written in base 5.

%H Giovanni Resta, <a href="/A071131/b071131.txt">Table of n, a(n) for n = 1..23</a> (terms < 5^33)

%e 268^2 = 71824 = 424|424|4 in base 5.

%e 1302084^2 = 1695422743056 = 210234211|210234211 in base 5.

%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[5, #] & /@ Range[15]) (* _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(5)-a(15) from _Giovanni Resta_, Aug 01 2018

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Last modified December 5 04:10 EST 2021. Contains 349530 sequences. (Running on oeis4.)