cp's OEIS Frontend

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

%I A032533 #37 Feb 21 2024 01:44:41
%S A032533 1,2,4,8,10,16,20,21,32,40,42,64,80,84,100,128,160,168,200,256,273,
%T A032533 320,336,400,512,546,640,672,800,1000,1024,1092,1280,1344,1600,2000,
%U A032533 2048,2184,2231,2510,2560,2688,2730,3200,3300,4000,4096,4368,4462
%N A032533 Numbers that, when expressed in base 2 and then interpreted in base 10, yield a multiple of the original number.
%C A032533 Note that A025612 is a subset of this sequence (numbers of form 2^i*10^j, with i, j >= 0).
%H A032533 Giovanni Resta, <a href="/A032533/b032533.txt">Table of n, a(n) for n = 1..1212</a> (terms < 3*10^11, first 251 terms from Paolo P. Lava)
%F A032533 A032533 = { m : m divides A007088(m) }. - _M. F. Hasler_, Oct 11 2019
%e A032533 8 in base 2 is 1000, which interpreted in base 10 is 1000 = 125*8.
%t A032533 Select[Range[10000], Mod[FromDigits[IntegerDigits[#, 2]], #] == 0 &] (* _Carl Najafi_, Aug 18 2011 *)
%o A032533 (Magma) [k:k in [1..5000]| Seqint(Intseq(k,2)) mod k eq 0]; // _Marius A. Burtea_, Oct 11 2019
%o A032533 (PARI) select( is_A032533(n)=fromdigits(binary(n))%n==0, [1..5000]) \\ _M. F. Hasler_, Oct 11 2019
%Y A032533 Cf. A032532, A032534, A007088.
%K A032533 nonn
%O A032533 1,2
%A A032533 _Patrick De Geest_, Apr 15 1998
%E A032533 Example and better description from _Erich Friedman_, Jul 21 2001
%E A032533 Edited by _Erich Friedman_, Feb 09 2002
%E A032533 Offset set to 1 by _Giovanni Resta_, Jul 13 2016
%E A032533 Name edited by _Jon E. Schoenfield_, Oct 25 2019