A358353 Numbers that are not of the form m + (sum of digits of m) + (product of digits of m) for any m.

1, 2, 4, 5, 7, 8, 10, 13, 16, 19, 25, 28, 31, 36, 37, 39, 40, 41, 45, 47, 49, 51, 52, 57, 59, 60, 61, 64, 65, 67, 70, 71, 72, 75, 79, 81, 84, 85, 87, 89, 91, 93, 94, 96, 100, 102, 116, 120, 125, 126, 129, 137, 141, 142, 146, 150, 152, 153, 160, 161, 162, 166, 171, 172, 173, 180

Offset

1,2

Comments

Numbers missing from A358350.

The first differences show some periodicity, for example those for values 2184-3811 repeat at terms 5513-7140. - Bill McEachen, Jan 08 2023

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for Colombian or self numbers and related sequences.

Example

There is no term du_10 < 36 such that du + (d+u) + (d*u) = 36, so 36 is a term.

Maple

f:= proc(n) local L; L:= convert(n, base, 10); n + convert(L, `+`)+convert(L, `*`) end proc:
sort(convert({$1..200} minus map(f, {$1..200}), list)); # Robert Israel, Dec 22 2022

Mathematica

f[n_] := n + Total[(d = IntegerDigits[n])] + Times @@ d; With[{m = 180}, Complement[Range[m], Table[f[n], {n, 1, m}]]] (* Amiram Eldar, Dec 19 2022 *)

Prog

(Python)
from math import prod
def sp(n): d = list(map(int, str(n))); return sum(d) + prod(d)
def ok(n): return all(m + sp(m) != n for m in range(n+1))
print([k for k in range(181) if ok(k)]) # Michael S. Branicky, Dec 19 2022
(PARI) f(n) = my(d=digits(n)); vecsum(d)+vecprod(d)+n; \\ A161351
isok(m) = for(i=1, m, if (f(i) == m, return(0))); return(1); \\ Michel Marcus, Jan 09 2023

Crossrefs

Cf. A161351, A358350, A358351, A358352.

Similar: A003052 (m+digitsum), A230104 (m+digitprod).

Sequence in context: A060686 A004214 A258376 * A353919 A231979 A072013

Adjacent sequences: A358350 A358351 A358352 * A358354 A358355 A358356

Keyword

nonn,base

Author

Bernard Schott, Dec 19 2022

Status

approved