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A343016 a(n) is the least nonnegative m such that m*n + A001414(n) is not prime.

%I A343016 #14 Apr 16 2021 00:18:15
%S A343016 0,1,1,0,1,5,1,0,0,2,1,4,1,0,0,0,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,2,
%T A343016 0,0,1,0,0,1,1,0,1,0,1,0,1,3,0,0,0,1,1,1,0,1,0,2,1,0,1,0,1,0,0,0,1,0,
%U A343016 0,0,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,6,0,0,0,0,0,2,1,0,1
%N A343016 a(n) is the least nonnegative m such that m*n + A001414(n) is not prime.
%C A343016 a(n) <= A001414(n).
%C A343016 a(n) = 0 iff n is not in A100118.
%C A343016 a(n) = 1 if n is prime.
%C A343016 a(n) >= 3 iff n is in A342302.
%H A343016 Robert Israel, <a href="/A343016/b343016.txt">Table of n, a(n) for n = 1..10000</a>
%e A343016 a(6) = 5 because A001414(6) = 5 and 5, 6+5=11, 2*6+5=17, 3*6+5=23, and 4*6+5=29 are prime but 5*6+5=35 is not.
%p A343016 f:= proc(n) local s, t, k;
%p A343016   s:= add(t[1]*t[2], t = ifactors(n)[2]);
%p A343016   for k from 0 do if not isprime(k*n+s) then return k fi od;
%p A343016 end proc:
%p A343016 map(f, [$1..100]);
%t A343016 Array[Block[{m = 0, k = Plus @@ Times @@@ FactorInteger[#]}, While[PrimeQ[# m + k], m++]; m] &, 105] (* _Michael De Vlieger_, Apr 13 2021 *)
%Y A343016 Cf. A001414, A100118, A342302.
%K A343016 nonn
%O A343016 1,6
%A A343016 _J. M. Bergot_ and _Robert Israel_, Apr 02 2021