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A242680 Numbers k dividing every cyclic permutation of k^3.

%I A242680 #13 Jun 04 2019 21:39:07
%S A242680 1,2,3,9,11,41,63,77,91,99,219,303,411,999,1353,5291,6363,6993,7777,
%T A242680 8547,9009,9191,9901,9999,12561,23661,41841,47027,75609,90243,99999,
%U A242680 110011,122859,124533,125341,152207,169983,170017,473211,487179,513513,575757,578369,626373,683527,703703,740259,904761,999001,999999,2463661,2709729,2754573
%N A242680 Numbers k dividing every cyclic permutation of k^3.
%C A242680 Includes k if 10^(d-1) <= k^3 < 10^d and k | 10^d-1.  Is 2 the only member of the sequence that is not of this form? - _Robert Israel_, Jun 04 2019
%H A242680 Robert Israel, <a href="/A242680/b242680.txt">Table of n, a(n) for n = 1..130</a>
%e A242680 41 is a term as the cyclic permutations of 41^3 = 68921 are {68921, 89216, 92168, 21689, 16892}
%e A242680 and
%e A242680   68921 = 41*1681;
%e A242680   89216 = 41*2176;
%e A242680   92168 = 41*2248;
%e A242680   21689 = 41*529;
%e A242680   16892 = 41*412.
%p A242680 filter:= proc(n) local d,t,r,i;
%p A242680   d:= ilog10(n^3);
%p A242680   t:= n^3;
%p A242680   for i from 1 to d do
%p A242680     r:= t mod 10;
%p A242680     t:= 10^d*r + (t-r)/10;
%p A242680     if not (t/n)::integer then return false fi;
%p A242680   od;
%p A242680   true
%p A242680 end proc:
%p A242680 select(filter, [$1..10^7]); # _Robert Israel_, Jun 04 2019
%t A242680 Select[Range[300000], And@@Divisible[FromDigits/@Table[ RotateRight[ IntegerDigits[ #^3], n], {n, IntegerLength[#^3]}], #]&]
%Y A242680 Cf. A178028.
%K A242680 nonn,base
%O A242680 1,2
%A A242680 _Michel Lagneau_, May 20 2014
%E A242680 More terms from _Robert Israel_, Jun 04 2019