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

1,3

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.

Links

Table of n, a(n) for n=1..70.

Prog

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

Crossrefs

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

Sequence in context: A317589 A141807 A246422 * A257671 A285523 A126968

Adjacent sequences: A072492 A072493 A072494 * A072496 A072497 A072498

Keyword

nonn,base

Author

Benoit Cloitre, Oct 19 2002

Extensions

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

Status

approved