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Automorphic numbers: numbers k such that k^21 ends with k. Also m-morphic numbers for any m such that (m-1)/10 is an even integer not divisible by 10.
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%I #26 Oct 09 2024 21:28:16

%S 0,1,2,3,4,5,6,7,8,9,11,12,13,16,17,19,21,23,24,25,27,28,29,31,32,33,

%T 36,37,39,41,43,44,47,48,49,51,52,53,56,57,59,61,63,64,67,68,69,71,72,

%U 73,75,76,77,79,81,83,84,87,88,89,91,92,93,96,97,99,101,107,125,143

%N Automorphic numbers: numbers k such that k^21 ends with k. Also m-morphic numbers for any m such that (m-1)/10 is an even integer not divisible by 10.

%C Definition: k is an m-morphic number if k^m ends with k. For this sequence m can be 21, 41, 61, ...

%C 3-morphic numbers = 7-morphic numbers, see A033819; 5-morphic numbers = 13-morphic numbers, see A068407.

%o (PARI) isok(n, m=21)={n == 0 || (n^m)%(10^(1+logint(n,10))) == n}

%Y Cf. A003226, A033819, A068407, A068408, A072496.

%K nonn,base

%O 1,3

%A _Benoit Cloitre_, Oct 19 2002

%E Missing terms inserted by _Sean A. Irvine_, Oct 05 2024