login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%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