A358350 Numbers that can be written as (m + sum of digits of m + product of digits of m) for some m.

3, 6, 9, 11, 12, 14, 15, 17, 18, 20, 21, 22, 23, 24, 26, 27, 29, 30, 32, 33, 34, 35, 38, 42, 43, 44, 46, 48, 50, 53, 54, 55, 56, 58, 62, 63, 66, 68, 69, 73, 74, 76, 77, 78, 80, 82, 83, 86, 88, 90, 92, 95, 97, 98, 99, 101, 103, 104, 105, 106, 107, 108, 109, 110

Offset: 1

Author

Bernard Schott, Nov 11 2022

Keywords

• nonn
• base

Comments

Integers that are in A161351.

(i) Can arbitrarily long sets of consecutive integers be found in this sequence?

(ii) Is the gap between two consecutive terms bounded?

A000533 \ {1} is a subsequence.

This has the same asymptotic density, approximately 0.9022222, as A176995, since the asymptotic density of non-pandigital numbers is 0. - Charles R Greathouse IV, Nov 16 2022

Examples

			A161351(23) = 23 + (2+3) + (2*3) = 34 so 34 is a term.
There is no integer du_10 such that du + (d+u) + (d*u) = 31, so 31 is not a term.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Range of A161351.

Similar: A176995 (m+digitsum), A336826 (m*digitprod), A337718 (m+digitprod).

Cf. A000533.

Programs

Mathematica

f[n_] := n + Total[(d = IntegerDigits[n])] + Times @@ d; With[{m = 110}, Select[Union[Table[f[n], {n, 1, m}]], # <= m &]] (* Amiram Eldar, Nov 11 2022 *)

PARI

f(n) = my(d=digits(n)); n + vecsum(d) + vecprod(d); \\ A161351
lista(nn) = select(x->(x<=nn), Set(vector(nn, k, f(k)))); \\ Michel Marcus, Nov 12 2022

Python

from math import prod
def sp(n): d = list(map(int, str(n))); return sum(d) + prod(d)
def ok(n): return any(m + sp(m) == n for m in range(n))
print([k for k in range(111) if ok(k)]) # Michael S. Branicky, Dec 19 2022

Formula

a(n) ~ kn with k approximately 1.108374, see comments. - Charles R Greathouse IV, Nov 16 2022