cp's OEIS Frontend

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

%I A358353 #30 Jan 16 2023 08:30:44
%S A358353 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,
%T A358353 60,61,64,65,67,70,71,72,75,79,81,84,85,87,89,91,93,94,96,100,102,116,
%U A358353 120,125,126,129,137,141,142,146,150,152,153,160,161,162,166,171,172,173,180
%N A358353 Numbers that are not of the form m + (sum of digits of m) + (product of digits of m) for any m.
%C A358353 Numbers missing from A358350.
%C A358353 The first differences show some periodicity, for example those for values 2184-3811 repeat at terms 5513-7140. - _Bill McEachen_, Jan 08 2023
%H A358353 Robert Israel, <a href="/A358353/b358353.txt">Table of n, a(n) for n = 1..10000</a>
%H A358353 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>.
%e A358353 There is no term du_10 < 36 such that du + (d+u) + (d*u) = 36, so 36 is a term.
%p A358353 f:= proc(n) local L; L:= convert(n,base,10); n + convert(L,`+`)+convert(L,`*`) end proc:
%p A358353 sort(convert({$1..200} minus map(f, {$1..200}),list)); # _Robert Israel_, Dec 22 2022
%t A358353 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 *)
%o A358353 (Python)
%o A358353 from math import prod
%o A358353 def sp(n): d = list(map(int, str(n))); return sum(d) + prod(d)
%o A358353 def ok(n): return all(m + sp(m) != n for m in range(n+1))
%o A358353 print([k for k in range(181) if ok(k)]) # _Michael S. Branicky_, Dec 19 2022
%o A358353 (PARI) f(n) = my(d=digits(n)); vecsum(d)+vecprod(d)+n; \\ A161351
%o A358353 isok(m) = for(i=1, m, if (f(i) == m, return(0))); return(1); \\ _Michel Marcus_, Jan 09 2023
%Y A358353 Cf. A161351, A358350, A358351, A358352.
%Y A358353 Similar: A003052 (m+digitsum), A230104 (m+digitprod).
%K A358353 nonn,base
%O A358353 1,2
%A A358353 _Bernard Schott_, Dec 19 2022