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

1,2

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.

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Subsequences: A011540, A047855 \ {1}.

Range of A230099.

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

Sequence in context: A092451 A214673 A055962 * A246410 A195169 A338922

Adjacent sequences: A337715 A337716 A337717 * A337719 A337720 A337721

Keyword

nonn,base

Author

Bernard Schott, Sep 16 2020

Status

approved