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A068408
Automorphic numbers: numbers k such that k^6 ends with k. Also m-morphic numbers for all m not congruent to 26 (mod 50) but congruent to 6 (mod 10).
5
0, 1, 5, 6, 16, 21, 25, 36, 41, 56, 61, 76, 81, 96, 176, 201, 376, 401, 576, 601, 625, 776, 801, 976, 1376, 2001, 3376, 4001, 5376, 6001, 7376, 8001, 9376, 20001, 29376, 40001, 49376, 60001, 69376, 80001, 89376, 90625, 109376, 200001, 309376, 400001, 509376
OFFSET
1,3
COMMENTS
90625^6 = 553972386755049228668212890625 hence 90625 is in the sequence.
MATHEMATICA
okQ[n_]:=Module[{idn=IntegerDigits[n], id6n=IntegerDigits[n^6]}, idn==Take[id6n, -Length[idn]]]
Select[Range[120000], okQ] (* Harvey P. Dale, Jan 16 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])
res = list(set(sum(morphs, []))); res.sort()
return res
# (call with pow=6 for this sequence), Eric M. Schmidt, Jul 29 2013
CROSSREFS
Cf. A033819.
Sequence in context: A058567 A115376 A076650 * A186696 A034454 A246715
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Mar 08 2002
EXTENSIONS
More terms from Eric M. Schmidt, Jul 29 2013
STATUS
approved