A337718 Numbers that can be written as (m + product of digits of m) for some m.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 23, 24, 26, 28, 29, 30, 32, 34, 35, 38, 40, 41, 42, 44, 45, 46, 47, 50, 54, 55, 56, 58, 60, 62, 65, 66, 67, 68, 70, 74, 75, 78, 80, 81, 85, 86, 88, 89, 90, 92, 94, 95, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109

Offset: 1

Author

Bernard Schott, Sep 16 2020

Keywords

• nonn
• base

Comments

Every integer that contains a digit 0 is a term (A011540).

When R_m with m >= 1 is in A002275, then R_m + 1 is a term (A047855 \ {1}).

Near similar:

-> Not-Colombian (A176995) are numbers that can be written as (m + sum of digits of m) for some m.

-> Bogotá numbers (A336826) are numbers that can be written as (m * product of digits of m) for some m.

Examples

			10 = 5 + 5 = 10 + (1*0) and 22 = 16 + (1*6) are terms.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequences: A011540, A047855 \ {1}.

Range of A230099.

Cf. A176995 (not Colombian), A336826 (Bogotá numbers).

Programs

Mathematica

m = 100; Select[Union[Table[n + Times @@ IntegerDigits[n], {n, 0, m}]], # <= m &] (* Amiram Eldar, Sep 16 2020 *)

PARI

isok(m) = {if (m==0, return (1)); for (k=1, m,  if (k+vecprod(digits(k)) == m, return (1)););} \\ Michel Marcus, Sep 17 2020

Python

from math import prod
def b(n): return n + prod(map(int, str(n)))
def aupto(n): return sorted(set(b(m) for m in range(n+1) if b(m) <= n))
print(aupto(109)) # Michael S. Branicky, Jan 09 2023