A029503 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 10 (most significant digit on right).

1, 2, 3, 5, 6, 9, 101, 107, 153, 167, 277, 414, 486, 858, 1659, 2894, 3093, 4299, 4842, 8838, 22734, 31869, 69492, 361057, 429786, 462018, 859002, 1170801, 1334667, 1663923, 6143512, 6162396, 6212646, 7034661, 8164443

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base
• more

Comments

This sequence differs from A061939 in that all least significant zeros are kept during concatenation.

Right concatenation, reverse order.

No more terms < 10^7. - Lars Blomberg, Oct 06 2011

Examples

			n = 22 is not a term since 12345678901112131415161718191021222 is not divisible by 22.
See A029495 for other examples.
		

Links

• Index entries for related sequences

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

Mathematica

b = 10; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, Reverse[IntegerDigits[#, b]]], b], #] &] (* Robert Price, Mar 12 2020 *)

PARI

isok(n) = my(s = ""); for (k=1, n, sk = digits(k); forstep (j=#sk, 1, -1, s = concat(s, sk[j]))); (eval(s) % n) == 0; \\ Michel Marcus, Jan 28 2017

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002

Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001

a(25)-a(35) from Lars Blomberg, Oct 06 2011