A068407 Automorphic numbers: numbers k such that k^5 ends with k. Also m-morphic numbers for all m > 5 such that m-1 is not divisible by 10 and m == 1 (mod 4).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 25, 32, 43, 49, 51, 57, 68, 75, 76, 93, 99, 125, 193, 249, 251, 307, 375, 376, 432, 443, 499, 501, 557, 568, 624, 625, 693, 749, 751, 807, 875, 943, 999, 1249, 1251, 1693, 1875, 2057, 2499, 2501, 2943, 3125, 3307, 3568, 3749, 3751

Offset

1,3

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Index entries for sequences related to automorphic numbers

Example

13568 is a term because 13568^5 = 459810807237016813568 ends with 13568.

Mathematica

Select[Range[0, 100000], PowerMod[#, 5, 10^IntegerLength[#]]==#&] (* Harvey P. Dale, Nov 04 2011 *)

Prog

(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])
    return sorted(set(sum(morphs, [])))
# (call with pow=5 for this sequence), Eric M. Schmidt, Jul 29 2013
(Magma) [n : n in [0..3749] | Intseq(n^5)[1..#Intseq(n)] eq Intseq(n)]; // Arkadiusz Wesolowski, Nov 15 2013

Crossrefs

Cf. A003226, A033819.

Sequence in context: A198044 A133134 A133505 * A334601 A117732 A116960

Adjacent sequences: A068404 A068405 A068406 * A068408 A068409 A068410

Keyword

nonn,base

Author

Benoit Cloitre, Mar 08 2002

Status

approved