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A242680 Numbers k dividing every cyclic permutation of k^3. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

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

EXAMPLE

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.

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]}], #]&]

CROSSREFS

Cf. A178028.

Sequence in context: A089645 A214259 A287680 * A275767 A088086 A088084

Adjacent sequences:  A242677 A242678 A242679 * A242681 A242682 A242683

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, May 20 2014

EXTENSIONS

More terms from Robert Israel, Jun 04 2019

STATUS

approved

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Last modified September 22 13:15 EDT 2021. Contains 347607 sequences. (Running on oeis4.)