A285829 Numbers n such that, for any i and j with i >= j >= 0, ds^i(n) divides ds^j(n) (where ds^k denotes the k-th iteration of the digital sum).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 198, 200, 201, 204, 207, 210, 216, 220, 222, 224, 225, 228, 230, 234, 240, 243, 252, 261, 264, 270, 280, 288, 300, 306, 312

Offset: 1

Author

Rémy Sigrist, Apr 27 2017

Keywords

• nonn
• base

Comments

All terms are Niven numbers (A005349).

All terms belongs to A234474; the first difference occurs at index 81: a(81) = 312 whereas A234474(81) = 308.

All powers of 10 belong to the sequence, hence the sequence is infinite.

Examples

			The digital sum of 312 is 6, and it divides 312; the digital sum of 6 is 6; hence 312 appears in the sequence.
The digital sum of 308 is 11, which divides 308; however the digital sum of 11 is 2, which does not divide 11; hence 308 is not in the sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005349, A234474.

Programs

PARI

is(n) = my (d=sumdigits(n)); if (n==d, return (1)); if (n%d, return (0)); return (is(d))