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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007088, A047778.

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

Sequence in context: A111794 A030290 A099088 * A212317 A161751 A354126

Adjacent sequences: A029444 A029445 A029446 * A029448 A029449 A029450

Keyword

nonn,base

Author

Olivier Gérard

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

Status

approved