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