A032533 Numbers that, when expressed in base 2 and then interpreted in base 10, yield a multiple of the original number.

1, 2, 4, 8, 10, 16, 20, 21, 32, 40, 42, 64, 80, 84, 100, 128, 160, 168, 200, 256, 273, 320, 336, 400, 512, 546, 640, 672, 800, 1000, 1024, 1092, 1280, 1344, 1600, 2000, 2048, 2184, 2231, 2510, 2560, 2688, 2730, 3200, 3300, 4000, 4096, 4368, 4462

Offset: 1

Author

Patrick De Geest, Apr 15 1998

Keywords

• nonn

Comments

Note that A025612 is a subset of this sequence (numbers of form 2^i*10^j, with i, j >= 0).

Examples

			8 in base 2 is 1000, which interpreted in base 10 is 1000 = 125*8.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1212 (terms < 3*10^11, first 251 terms from Paolo P. Lava)

Crossrefs

Cf. A032532, A032534, A007088.

Programs

Magma

[k:k in [1..5000]| Seqint(Intseq(k,2)) mod k eq 0]; // Marius A. Burtea, Oct 11 2019

Mathematica

Select[Range[10000], Mod[FromDigits[IntegerDigits[#, 2]], #] == 0 &] (* Carl Najafi, Aug 18 2011 *)

PARI

select( is_A032533(n)=fromdigits(binary(n))%n==0, [1..5000]) \\ M. F. Hasler, Oct 11 2019

Formula

A032533 = { m : m divides A007088(m) }. - M. F. Hasler, Oct 11 2019

Extensions

Example and better description from Erich Friedman, Jul 21 2001

Edited by Erich Friedman, Feb 09 2002

Offset set to 1 by Giovanni Resta, Jul 13 2016

Name edited by Jon E. Schoenfield, Oct 25 2019