

A337718


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


6



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
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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:
> NotColombian (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



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))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



