A029447 Numbers k that divide the (right) concatenation of all numbers <= k written in base 2 (most significant digit on left).

1, 2, 3, 4, 5, 7, 8, 16, 26, 32, 38, 40, 46, 64, 96, 128, 138, 192, 228, 256, 512, 640, 1024, 2048, 4096, 4192, 4766, 4790, 5142, 5952, 6144, 6866, 8122, 8192, 8448, 10240, 11283, 11392, 12288, 14780, 15360, 15744, 16384, 17408, 20841, 20866, 32768, 58496, 59104

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base

Comments

All powers of 2 are in the sequence. - Chai Wah Wu, Nov 10 2014

Numbers k that divide A047778(k). - Michel Marcus, Nov 11 2014

Examples

			3 is in the sequence because the concatenation is 1 10 11, binary expansion of 27, that is divisible by 3.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..54

Crossrefs

Cf. A007088, A047778.

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

Programs

Mathematica

Select[Range[2^13], Mod[FromDigits[Flatten[IntegerDigits[#, 2] & /@ Range@ #], 2], #] == 0 &] (* Michael De Vlieger, Aug 29 2015 *)

PARI

lista(nn) = {vs = []; for (n=1, nn, vs = concat(vs, binary(n)); val = subst(Pol(vs), x, 2); if (val % n == 0, print1(n, ", ")););} \\ Michel Marcus, Nov 11 2014

Extensions

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

More terms from David W. Wilson

a(47)-a(49) from Chai Wah Wu, Nov 10 2014