|
%I #13 Aug 01 2018 21:08:26
%S 69696,56722567225,95540955409,1108033241108033241,
%T 1220096161220096161,4312080784312080784,4432132964432132964,
%U 4880384644880384644,9024307889024307889,9972299169972299169,225607697225607697225,946308825294630882529,1322314049613223140496
%N Squares which repeat with at least two full periods when written in base 10.
%H Giovanni Resta, <a href="/A069919/b069919.txt">Table of n, a(n) for n = 1..21</a> (terms < 10^24)
%e 264^2 = 69|69|6 in base 10.
%e 15020242915^2 = 225607697|225607697|225 in base 10.
%e 36363636364^2 = 13223140496|13223140496 in base 10.
%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[10, #] & /@ Range[11]) (* _Giovanni Resta_, Aug 01 2018 *)
%Y Cf. A071128 (base 2) - A071135 (base 9), A116502.
%K base,nonn
%O 1,1
%A _Erich Friedman_, Apr 25 2002
%E Corrected and extended by _Jason Earls_, Jun 16 2002
%E Data corrected and extended by _Giovanni Resta_, Aug 01 2018
|
