A326806 Numbers k such that k multiplied by the sum of all its digits contains k as a substring.

0, 1, 5, 6, 10, 19, 28, 37, 46, 50, 55, 60, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 208, 217, 226, 235, 244, 253, 262, 271, 280, 307, 316, 325, 334, 343, 352, 361, 370, 406, 415, 424, 433, 442, 451, 460, 500, 505, 514, 523, 532

Offset: 1

Author

Alois P. Heinz, Oct 19 2019

Keywords

• nonn
• base

Comments

Inspired by A328095.

Contains all numbers whose digit sum is a power of 10.

Contains all numbers of the form 5*10^k and 6*10^k. Terms which are not in the sets above are: 0, 6667, 58824, 8823529412, ... - Chai Wah Wu, Oct 19 2019

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A011557, A326811, A328095.

Programs

Maple

a:= proc(n) option remember; local k; if n=1 then 0 else
      for k from 1+a(n-1) while searchtext(cat(k), cat(k*
      add(i, i=convert(k, base, 10))))=0 do od: k fi
    end:
seq(a(n), n=1..75);

Python

n, A326806_list = 0, []
while len(A326806_list) < 10000:
    sn = str(n)
    if sn in str(n*sum(int(d) for d in sn)):
        A326806_list.append(n)
    n += 1 # Chai Wah Wu, Oct 19 2019