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

1,1

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Range of A161351.

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

Cf. A000533.

Sequence in context: A340491 A329511 A065940 * A024795 A000408 A025321

Adjacent sequences: A358347 A358348 A358349 * A358351 A358352 A358353

Keyword

nonn,base

Author

Bernard Schott, Nov 11 2022

Status

approved