cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A071133 Squares which repeat with at least two full periods when written in base 7.

This page as a plain text file.
%I A071133 #5 Aug 01 2018 10:28:39
%S A071133 16,400,900,1600,29584,70627216,394618225,2214643600,4982948100,
%T A071133 8858574400,16052636601,64210546404,169556179984,727092173809,
%U A071133 1120597967889,2908368695236,6543829564281,6703226505481,79822717134736,407103419654416,12766762698010000
%N A071133 Squares which repeat with at least two full periods when written in base 7.
%H A071133 Giovanni Resta, <a href="/A071133/b071133.txt">Table of n, a(n) for n = 1..39</a> (terms < 7^29)
%e A071133 19865^2 = 394618225 = 12531|12531|1 in base 7.
%e A071133 411772^2 = 169556179984 = 1515152|1515152 in base 7.
%t A071133 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 A071133 Cf. A071128 (base 2) - A071135 (base 9), A069919 (base 10).
%K A071133 base,nonn
%O A071133 1,1
%A A071133 _Erich Friedman_, May 28 2002
%E A071133 a(17)-a(21) from _Giovanni Resta_, Aug 01 2018