login
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).
6
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
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
Sequence in context: A198044 A133134 A133505 * A334601 A117732 A116960
KEYWORD
nonn,base
AUTHOR
Benoit Cloitre, Mar 08 2002
STATUS
approved