A262814 Numbers k dividing every cyclic permutation of k^k.

1, 2, 3, 7, 9, 11, 27, 63, 99, 111, 129, 159, 231, 271, 273, 303, 333, 351, 357, 403, 457, 711, 991, 999, 1111, 1147, 1241, 2121, 2479, 4227, 4653, 5151, 5547, 5837, 6191, 6237, 6643, 6993, 7133, 8229, 8547, 8683, 8811, 8987, 9009, 9633, 9999, 11009, 13449, 13531

Offset

1,2

Comments

Conjecture: 10^n-1 is a term of the sequence for all n > 0. - Chai Wah Wu, Nov 03 2015

Links

Chai Wah Wu, Table of n, a(n) for n = 1..100

Example

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.

Mathematica

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

Prog

(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
(Python)
A262814_list = []
for k in range(1, 10**3):
    n = k**k
    if not n % k:
        s = str(n)
        for i in range(len(s)-1):
            s = s[1:]+s[0]
            if int(s) % k:
                break
        else:
            A262814_list.append(k) # Chai Wah Wu, Oct 26 2015

Crossrefs

Cf. A178028, A242680, A242740.

Sequence in context: A203234 A212985 A103797 * A328982 A260641 A077510

Adjacent sequences: A262811 A262812 A262813 * A262815 A262816 A262817

Keyword

nonn,base

Author

Michel Lagneau, Oct 03 2015

Extensions

a(24)-a(27) from Michel Marcus, Oct 11 2015

a(28)-a(50) from Chai Wah Wu, Oct 26 2015

Status

approved