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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).

%I A068408 #25 Mar 06 2020 09:26:42
%S A068408 0,1,5,6,16,21,25,36,41,56,61,76,81,96,176,201,376,401,576,601,625,
%T A068408 776,801,976,1376,2001,3376,4001,5376,6001,7376,8001,9376,20001,29376,
%U A068408 40001,49376,60001,69376,80001,89376,90625,109376,200001,309376,400001,509376
%N 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).
%C A068408 90625^6 = 553972386755049228668212890625 hence 90625 is in the sequence.
%H A068408 Eric M. Schmidt, <a href="/A068408/b068408.txt">Table of n, a(n) for n = 1..1000</a>
%H A068408 <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>
%t A068408 okQ[n_]:=Module[{idn=IntegerDigits[n],id6n=IntegerDigits[n^6]}, idn==Take[id6n,-Length[idn]]]
%t A068408 Select[Range[120000],okQ]  (* _Harvey P. Dale_, Jan 16 2011 *)
%o A068408 (Sage)
%o A068408 def automorphic(maxdigits, pow, base=10) :
%o A068408     morphs = [[0]]
%o A068408     for i in range(maxdigits):
%o A068408         T=[d*base^i+x for x in morphs[-1] for d in range(base)]
%o A068408         morphs.append([x for x in T if x^pow % base^(i+1) == x])
%o A068408     res = list(set(sum(morphs,[]))); res.sort()
%o A068408     return res
%o A068408 # (call with pow=6 for this sequence), _Eric M. Schmidt_, Jul 29 2013
%Y A068408 Cf. A033819.
%K A068408 easy,nonn
%O A068408 1,3
%A A068408 _Benoit Cloitre_, Mar 08 2002
%E A068408 More terms from _Eric M. Schmidt_, Jul 29 2013