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).

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

Author

Benoit Cloitre, Mar 08 2002

Keywords

• easy
• nonn

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

Crossrefs

Cf. A033819.

Programs

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 *)

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

Extensions

More terms from Eric M. Schmidt, Jul 29 2013