A061955 Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 2 (most significant digit on right).

1, 3, 7, 29, 375, 545, 971, 1643, 37801, 435805, 554423, 565947, 645915, 733533, 871927, 9703985

Offset: 1

Author

Larry Reeves (larryr(AT)acm.org), May 24 2001

Keywords

• nonn
• base
• more

Comments

This sequence differs from A029519 in that all least significant zeros are kept during concatenation.

No more terms < 10^7. - Lars Blomberg, Aug 31 2011

Examples

			7654321 -> (111)(011)(101)(001)(11)(01)(1) base 2 ->11101110100111011 base 2 = 122171 and 7 divides 122171.
		

Links

• Index entries for related sequences

Crossrefs

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

Programs

Mathematica

b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[Reverse[IntegerDigits[#, b]], c], b], #] &] (* Robert Price, Mar 07 2020 *)

PARI

is(n) = my(t=[]); for(k=1, n, t=concat(Vecrev(binary(k)), t)); if(Mod(subst(Pol(t), x, 2), n)==0, return(1), return(0)) \\ Felix Fröhlich, Jul 06 2017

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002; Aug 25 2002

a(13)-a(16) from Lars Blomberg, Aug 31 2011