A072495 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.

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, 36, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 56, 57, 59, 61, 63, 64, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 83, 84, 87, 88, 89, 91, 92, 93, 96, 97, 99, 101, 107, 125, 143

Offset: 1

Author

Benoit Cloitre, Oct 19 2002

Keywords

• nonn
• base

Comments

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

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

Crossrefs

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

Programs

PARI

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

Extensions

Missing terms inserted by Sean A. Irvine, Oct 05 2024