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