A262814 - OEIS

%I #21 Nov 05 2015 11:22:07

%S 1,2,3,7,9,11,27,63,99,111,129,159,231,271,273,303,333,351,357,403,

%T 457,711,991,999,1111,1147,1241,2121,2479,4227,4653,5151,5547,5837,

%U 6191,6237,6643,6993,7133,8229,8547,8683,8811,8987,9009,9633,9999,11009,13449,13531

%N Numbers k dividing every cyclic permutation of k^k.

%C Conjecture: 10^n-1 is a term of the sequence for all n > 0. - _Chai Wah Wu_, Nov 03 2015

%H Chai Wah Wu, <a href="/A262814/b262814.txt">Table of n, a(n) for n = 1..100</a>

%e 7 is a member as the six cyclic permutations of 7^7 = 823543 are {823543, 382354, 438235, 543823, 354382, 235438} and these 6 integers are divisible by 7.

%t Select[Range[1000], And@@Divisible[FromDigits/@Table[ RotateRight[ IntegerDigits[ #^#], n], {n, IntegerLength[#^#]}], #]&]

%o (PARI) isok(n) = {my(nn = n^n); for (j=1, #Str(nn)-1, cp = eval(Str(nn%10^j, nn\10^j)); if (cp % n, return (0));); return (1);} \\ _Michel Marcus_, Oct 11 2015

%o (Python)

%o A262814_list = []

%o for k in range(1,10**3):

%o     n = k**k

%o     if not n % k:

%o         s = str(n)

%o         for i in range(len(s)-1):

%o             s = s[1:]+s[0]

%o             if int(s) % k:

%o                 break

%o         else:

%o             A262814_list.append(k) # _Chai Wah Wu_, Oct 26 2015

%Y Cf. A178028, A242680, A242740.

%K nonn,base

%O 1,2

%A _Michel Lagneau_, Oct 03 2015

%E a(24)-a(27) from _Michel Marcus_, Oct 11 2015

%E a(28)-a(50) from _Chai Wah Wu_, Oct 26 2015