A248040 Numbers n such that n*digsum(n) contains the same distinct digits as n.

1, 10, 100, 109, 190, 208, 280, 307, 370, 406, 450, 460, 505, 550, 604, 640, 703, 730, 802, 820, 901, 910, 1000, 1009, 1018, 1027, 1036, 1045, 1054, 1063, 1072, 1081, 1090, 1108, 1168, 1180, 1207, 1270, 1286, 1306, 1360, 1405, 1450, 1504, 1540, 1603, 1630, 1702, 1720, 1726, 1801

Offset: 1

Author

Derek Orr, Sep 30 2014

Keywords

• nonn
• base
• easy

Comments

10^k is a subsequence for k >= 0. Thus this sequence is infinite.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953 (sum of digits), A011557 (powers of 10).

Cf. A247888 (similar, with n + product of digits), A247887 (similar, with n + digsum).

Programs

Maple

filter:= proc(n) local L,s,d;
  L:= convert(n,base,10);
  d:= convert(L,set);
  s:= convert(L,`+`);
  evalb(convert(convert(n*s,base,10),set)=d)
end proc:
select(filter, [$1..2000]); # Robert Israel, Mar 06 2018

PARI

for(n=1,10^4,d=digits(n);if(vecsort(d,,8)==vecsort(digits(n*sumdigits(n)),,8),print1(n,", ")))