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Numbers n dividing every cyclic permutation of n^4.
1

%I #5 May 21 2014 20:36:49

%S 1,3,9,21,27,73,99,111,271,693,707,777,819,909,999,2151,2629,3441,

%T 3813,4551,6987,7227,7373,9999,18981,19019,20007,20979,23199,24453,

%U 25641,27027,27417,30303,81819,82113,83883,99999,125523,172013,194841,201917,238139

%N Numbers n dividing every cyclic permutation of n^4.

%C Property of the sequence :

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

%C a(1) = A178028 (1) = 1;

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

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

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

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

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

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

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

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

%C ...........................

%e 21 is a member as all the six cyclic permutations of 21^4 = 194481 are :

%e {194481, 944811, 448119, 481194, 811944, 119448} and :

%e 194481 = 21*9261;

%e 944811 = 21*44991;

%e 448119 = 21*21339;

%e 811944 = 21*38664;

%e 119448 = 21*5688.

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

%Y Cf. A178028, A242680.

%K nonn,base

%O 1,2

%A _Michel Lagneau_, May 21 2014