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

1, 2, 3, 9, 11, 41, 63, 77, 91, 99, 219, 303, 411, 999, 1353, 5291, 6363, 6993, 7777, 8547, 9009, 9191, 9901, 9999, 12561, 23661, 41841, 47027, 75609, 90243, 99999, 110011, 122859, 124533, 125341, 152207, 169983, 170017, 473211, 487179, 513513, 575757, 578369, 626373, 683527, 703703, 740259, 904761, 999001, 999999, 2463661, 2709729, 2754573

Offset: 1

Author

Michel Lagneau, May 20 2014

Keywords

• nonn
• base

Comments

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

Examples

			41 is a term as the cyclic permutations of 41^3 = 68921 are {68921, 89216, 92168, 21689, 16892}
and
  68921 = 41*1681;
  89216 = 41*2176;
  92168 = 41*2248;
  21689 = 41*529;
  16892 = 41*412.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..130

Crossrefs

Cf. A178028.

Programs

Maple

filter:= proc(n) local d,t,r,i;
  d:= ilog10(n^3);
  t:= n^3;
  for i from 1 to d do
    r:= t mod 10;
    t:= 10^d*r + (t-r)/10;
    if not (t/n)::integer then return false fi;
  od;
  true
end proc:
select(filter, [$1..10^7]); # Robert Israel, Jun 04 2019

Mathematica

Select[Range[300000], And@@Divisible[FromDigits/@Table[ RotateRight[ IntegerDigits[ #^3], n], {n, IntegerLength[#^3]}], #]&]

Extensions

More terms from Robert Israel, Jun 04 2019