cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A029447 #31 Jan 14 2025 10:23:41
%S A029447 1,2,3,4,5,7,8,16,26,32,38,40,46,64,96,128,138,192,228,256,512,640,
%T A029447 1024,2048,4096,4192,4766,4790,5142,5952,6144,6866,8122,8192,8448,
%U A029447 10240,11283,11392,12288,14780,15360,15744,16384,17408,20841,20866,32768,58496,59104
%N A029447 Numbers k that divide the (right) concatenation of all numbers <= k written in base 2 (most significant digit on left).
%C A029447 All powers of 2 are in the sequence. - _Chai Wah Wu_, Nov 10 2014
%C A029447 Numbers k that divide A047778(k). - _Michel Marcus_, Nov 11 2014
%H A029447 Chai Wah Wu, <a href="/A029447/b029447.txt">Table of n, a(n) for n = 1..54</a>
%e A029447 3 is in the sequence because the concatenation is 1 10 11, binary expansion of 27, that is divisible by 3.
%t A029447 Select[Range[2^13], Mod[FromDigits[Flatten[IntegerDigits[#, 2] & /@ Range@ #], 2], #] == 0 &] (* _Michael De Vlieger_, Aug 29 2015 *)
%o A029447 (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 A029447 Cf. A007088, A047778.
%Y A029447 Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.
%K A029447 nonn,base
%O A029447 1,2
%A A029447 _Olivier Gérard_
%E A029447 More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
%E A029447 More terms from _David W. Wilson_
%E A029447 a(47)-a(49) from _Chai Wah Wu_, Nov 10 2014