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
Examples
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.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..100
Programs
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Mathematica
Select[Range[1000], And@@Divisible[FromDigits/@Table[ RotateRight[ IntegerDigits[ #^#], n], {n, IntegerLength[#^#]}], #]&] -
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
Extensions
a(24)-a(27) from Michel Marcus, Oct 11 2015
a(28)-a(50) from Chai Wah Wu, Oct 26 2015
Comments