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

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, 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, 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

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 02 2021

Keywords

• nonn

Comments

a(n) <= A001414(n).

a(n) = 0 iff n is not in A100118.

a(n) = 1 if n is prime.

a(n) >= 3 iff n is in A342302.

Examples

			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.
		

Links

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

Crossrefs

Cf. A001414, A100118, A342302.

Programs

Maple

f:= proc(n) local s, t, k;
  s:= add(t[1]*t[2], t = ifactors(n)[2]);
  for k from 0 do if not isprime(k*n+s) then return k fi od;
end proc:
map(f, [$1..100]);

Mathematica

Array[Block[{m = 0, k = Plus @@ Times @@@ FactorInteger[#]}, While[PrimeQ[# m + k], m++]; m] &, 105] (* Michael De Vlieger, Apr 13 2021 *)