A029447 - OEIS

%I #31 Jan 14 2025 10:23:41

%S 1,2,3,4,5,7,8,16,26,32,38,40,46,64,96,128,138,192,228,256,512,640,

%T 1024,2048,4096,4192,4766,4790,5142,5952,6144,6866,8122,8192,8448,

%U 10240,11283,11392,12288,14780,15360,15744,16384,17408,20841,20866,32768,58496,59104

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

%C All powers of 2 are in the sequence. - _Chai Wah Wu_, Nov 10 2014

%C Numbers k that divide A047778(k). - _Michel Marcus_, Nov 11 2014

%H Chai Wah Wu, <a href="/A029447/b029447.txt">Table of n, a(n) for n = 1..54</a>

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

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

%o (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

%Y Cf. A007088, A047778.

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

%K nonn,base

%O 1,2

%A _Olivier Gérard_

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

%E More terms from _David W. Wilson_

%E a(47)-a(49) from _Chai Wah Wu_, Nov 10 2014