A032543 - OEIS

%I #30 Oct 25 2019 18:11:15

%S 0,1,2,3,4,5,10,15,20,25,50,75,100,125,160,224,237,250,320,330,375,

%T 490,500,625,800,1000,1120,1185,1250,1600,1650,1875,2450,2500,3125,

%U 3800,4000,4704,5000,5600,5925,6250,7600,8000,8250,9375,10000,12250

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

%C From _Robert Israel_, Apr 10 2016: (Start)

%C n for which n divides A007091(n).

%C If n is in the sequence, then so is 5*n. (End)

%H 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 25 in base 5 is 100, which interpreted in base 10 is 100 = 4 * 25.

%e 224 in base 5 is 1344, which interpreted in base 10 is 1344 = 6 * 224.

%p filter:= proc(n) local L,i;

%p L:= convert(n,base,5);

%p add(L[i]*10^(i-1),i=1..nops(L)) mod n = 0

%p end proc:

%p 0, op(select(filter, [$1..10^5])); # _Robert Israel_, Apr 10 2016

%t Select[Range[0,13000], Divisible[FromDigits[IntegerDigits[#, 5]], #] &] (* _Harvey P. Dale_, Feb 01 2011 *)

%Y Cf. A007091, A032542, A032544.

%K nonn,base

%O 1,3

%A _Patrick De Geest_, Apr 15 1998

%E Example and better description from _Erich Friedman_, Jul 21 2001

%E Edited by _Erich Friedman_, Feb 09 2002

%E Offset changed and 0 inserted by _Robert Israel_, Apr 11 2016

%E Name edited by _Jon E. Schoenfield_, Oct 25 2019