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A068408 Automorphic numbers: n^6 ends with n. Also m-morphic numbers for all m not equal to 26 (mod 50) but equal to 6 (mod 10). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

90625^6 = 553972386755049228668212890625 hence 90625 is in the sequence.

LINKS

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

Index entries for sequences related to automorphic numbers

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 xrange(maxdigits):

........T=[d*base^i+x for x in morphs[-1] for d in xrange(base)]

........morphs.append([x for x in T if x^pow % base^(i+1) == x])

....res = list(set(sum(morphs, []))); res.sort()

....return res

end # (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

Adjacent sequences:  A068405 A068406 A068407 * A068409 A068410 A068411

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 08 2002

EXTENSIONS

More terms from Eric M. Schmidt, Jul 29 2013

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)