A242740 Numbers n dividing every cyclic permutation of n^4.

1, 3, 9, 21, 27, 73, 99, 111, 271, 693, 707, 777, 819, 909, 999, 2151, 2629, 3441, 3813, 4551, 6987, 7227, 7373, 9999, 18981, 19019, 20007, 20979, 23199, 24453, 25641, 27027, 27417, 30303, 81819, 82113, 83883, 99999, 125523, 172013, 194841, 201917, 238139

Offset: 1

Author

Michel Lagneau, May 21 2014

Keywords

• nonn
• base

Comments

Property of the sequence :

Consider the sequence A178028 (Numbers n dividing every cyclic permutation of n^2), so

a(1) = A178028 (1) = 1;

a(5) = A178028 (5) = 27;

a(7) = A178028 (7) = 99;

a(9) = A178028 (9) = 271;

a(10) = A178028 (15) = 693;

a(13) = A178028 (17) = 819;

a(15) = A178028 (18) = 999;

a(16) = A178028 (19) = 2151;

a(22) = A178028 (22) = 7227;

...........................

Examples

			21 is a member as all the six cyclic permutations of 21^4 = 194481 are :
{194481, 944811, 448119, 481194, 811944, 119448} and :
194481 = 21*9261;
944811 = 21*44991;
448119 = 21*21339;
811944 = 21*38664;
119448 = 21*5688.
		

Crossrefs

Cf. A178028, A242680.

Programs

Mathematica

Select[Range[300000], And@@Divisible[FromDigits/@Table[ RotateRight[ IntegerDigits[ #^4], n], {n, IntegerLength[#^4]}], #]&]