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

1,3

Comments

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

Links

Table of n, a(n) for n=1..60.

Prog

(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

Crossrefs

Cf. A072495.

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

Sequence in context: A195993 A334457 A010456 * A306482 A047431 A288695

Adjacent sequences: A072493 A072494 A072495 * A072497 A072498 A072499

Keyword

nonn

Author

Benoit Cloitre, Oct 19 2002

Extensions

Sequence corrected by Eric M. Schmidt, Jul 30 2013

Status

approved