A029484 Numbers k that divide the (left) concatenation of all numbers <= k written in base 15 (most significant digit on left).

1, 7, 32, 49, 61, 91, 169, 224, 791, 1568, 10304, 34112, 160832, 733376, 966721, 1127392, 4197571, 10914848, 13250272, 15000608, 62776133, 70412363, 82053664, 138391456, 198795233, 211659392, 272510336, 484441216, 1448538133, 1846451173, 2444373281, 2681439341, 11942145152, 22206078181, 25210297984

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base

Comments

No other terms below 3*10^10.

No multiple of 3 or 5 can be in this sequence, since the numbers resulting from these concatenations are all congruent to 1 mod 15. - Alonso del Arte, Sep 16 2016

Examples

			In base 15, 7654321 is 84557956 in decimal, and we verify that this is a multiple of 7, as 84557956/7 = 12079708. Hence 7 is in the sequence.
87654321 base 15 is 1451432956 and 1451432956/8 = 181429119.5. Hence 8 is not in the sequence.
		

Links

• Index entries for related sequences

Crossrefs

Cf. A029447-A029470 (in particular, A029460), A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

Mathematica

Select[Range[10^3], Divisible[FromDigits[#, 15] &@ Flatten@ Reverse@ IntegerDigits[Range@ #, 15], #] &] (* Michael De Vlieger, Sep 16 2016 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 01 2001

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

a(14)-a(23) from Max Alekseyev, May 15 2011

a(24)-a(35) from Jason Yuen, Jun 05 2024