A072496 k-morphic numbers for any k such that (k-1)/10 is an odd integer not divisible by 5.

0, 1, 4, 5, 6, 9, 11, 16, 19, 21, 24, 25, 29, 31, 36, 39, 41, 44, 49, 51, 56, 59, 61, 64, 69, 71, 75, 76, 79, 81, 84, 89, 91, 96, 99, 101, 125, 149, 151, 176, 199, 201, 224, 249, 251, 299, 301, 349, 351, 375, 376, 399, 401, 424, 449, 451, 499, 501, 549, 551

Offset: 1

Author

Benoit Cloitre, Oct 19 2002

Keywords

• nonn

Comments

Definition: n is a k-morphic number if n^k ends with n.

Crossrefs

Cf. A072495.

3-morphic numbers = 7-morphic numbers, see A033819; 5-morphic numbers = 13-morphic numbers, see A068407.

Programs

PARI

k=11; for(n=1,10000,if((n^k)%(10^ceil(log(n)/log(10)))==n, print1(n,","))); \\ starting with 4, 5, ...

Sage

def automorphic(maxdigits, pow, base=10) :
    morphs = [[0]]
    for i in range(maxdigits):
        T=[d*base^i+x for x in morphs[-1] for d in range(base)]
        morphs.append([x for x in T if x^pow % base^(i+1) == x])
    res = list(set(sum(morphs, []))); res.sort()
    return res
# (call with pow=11 for this sequence), Eric M. Schmidt, Jul 30 2013

Extensions

Sequence corrected by Eric M. Schmidt, Jul 30 2013