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

1,2

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(Magma) [k:k in [1..5000]| Seqint(Intseq(k, 2)) mod k eq 0]; // Marius A. Burtea, Oct 11 2019
(PARI) select( is_A032533(n)=fromdigits(binary(n))%n==0, [1..5000]) \\ M. F. Hasler, Oct 11 2019

Crossrefs

Cf. A032532, A032534, A007088.

Sequence in context: A093886 A352203 A125732 * A062884 A026169 A177931

Adjacent sequences: A032530 A032531 A032532 * A032534 A032535 A032536

Keyword

nonn

Author

Patrick De Geest, Apr 15 1998

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

Status

approved