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A032533
Numbers that, when expressed in base 2 and then interpreted in base 10, yield a multiple of the original number.
11
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
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