A032540 Numbers that, when expressed in base 4 and then interpreted in base 10, yield a multiple of the original number.

0, 1, 2, 3, 6, 24, 120, 171, 177, 273, 362, 440, 546, 819, 1418, 1560, 1582, 1638, 1760, 1806, 2400, 2841, 2927, 3640, 4706, 4882, 5720, 6328, 6552, 7040, 7224, 9431, 9600, 10101, 14560, 20202, 22880, 24800, 25080, 25312, 28896, 32760, 36974, 38400

Offset: 1

Author

Patrick De Geest, Apr 15 1998

Keywords

• base
• nonn

Comments

n such that A007090(n) is a multiple of n. - Robert Israel, Sep 13 2018

Examples

			24 in base 4 is 120, which interpreted in base 10 is 120 = 5*24.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..153 (terms < 5*10^12, first 100 terms from Robert Israel)

Crossrefs

Cf. A032539, A032541, A032532.

Programs

Maple

filter:= proc(n) local L,t;
  L:= convert(n,base,4);
  t:= add(L[i]*10^(i-1),i=1..nops(L));
  t mod n = 0
end proc:
filter(0):=true:
select(filter, [$0..10^5]); # Robert Israel, Sep 13 2018

Mathematica

Join[{0}, Select[Range[40000], Divisible[FromDigits[IntegerDigits[#,4]], #]&]]  (* Harvey P. Dale, Apr 20 2011 *)

Extensions

More terms from Erich Friedman and Naohiro Nomoto, Aug 06 2001

Offset changed by Robert Israel, Sep 13 2018

Name edited by Jon E. Schoenfield, Oct 25 2019