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

1,6

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001414, A100118, A342302.

Sequence in context: A371761 A269129 A320606 * A058177 A345373 A204619

Adjacent sequences: A343013 A343014 A343015 * A343017 A343018 A343019

Keyword

nonn

Author

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

Status

approved