cp's OEIS Frontend

A032543 Numbers that, when expressed in base 5 and then interpreted in base 10, yield a multiple of the original number.

%I A032543 #30 Oct 25 2019 18:11:15
%S A032543 0,1,2,3,4,5,10,15,20,25,50,75,100,125,160,224,237,250,320,330,375,
%T A032543 490,500,625,800,1000,1120,1185,1250,1600,1650,1875,2450,2500,3125,
%U A032543 3800,4000,4704,5000,5600,5925,6250,7600,8000,8250,9375,10000,12250
%N A032543 Numbers that, when expressed in base 5 and then interpreted in base 10, yield a multiple of the original number.
%C A032543 From _Robert Israel_, Apr 10 2016: (Start)
%C A032543 n for which n divides A007091(n).
%C A032543 If n is in the sequence, then so is 5*n. (End)
%H A032543 Giovanni Resta, <a href="/A032543/b032543.txt">Table of n, a(n) for n = 1..577</a> (terms < 5*10^12, first 147 terms from Robert Israel)
%e A032543 25 in base 5 is 100, which interpreted in base 10 is 100 = 4 * 25.
%e A032543 224 in base 5 is 1344, which interpreted in base 10 is 1344 = 6 * 224.
%p A032543 filter:= proc(n) local L,i;
%p A032543 L:= convert(n,base,5);
%p A032543 add(L[i]*10^(i-1),i=1..nops(L)) mod n = 0
%p A032543 end proc:
%p A032543 0, op(select(filter, [$1..10^5])); # _Robert Israel_, Apr 10 2016
%t A032543 Select[Range[0,13000], Divisible[FromDigits[IntegerDigits[#, 5]], #] &] (* _Harvey P. Dale_, Feb 01 2011 *)
%Y A032543 Cf. A007091, A032542, A032544.
%K A032543 nonn,base
%O A032543 1,3
%A A032543 _Patrick De Geest_, Apr 15 1998
%E A032543 Example and better description from _Erich Friedman_, Jul 21 2001
%E A032543 Edited by _Erich Friedman_, Feb 09 2002
%E A032543 Offset changed and 0 inserted by _Robert Israel_, Apr 11 2016
%E A032543 Name edited by _Jon E. Schoenfield_, Oct 25 2019