A343691 a(n) is the least prime p such that p + A014574(n) is prime.

3, 5, 5, 5, 7, 5, 7, 7, 5, 5, 11, 7, 11, 5, 13, 5, 11, 7, 11, 5, 5, 11, 7, 5, 19, 7, 7, 13, 5, 13, 11, 5, 11, 5, 5, 11, 7, 11, 7, 5, 11, 7, 5, 7, 5, 7, 5, 7, 5, 5, 5, 7, 29, 11, 11, 13, 5, 11, 17, 23, 5, 11, 5, 11, 17, 7, 11, 5, 5, 23, 7, 7, 7, 17, 5, 5, 7, 11, 7, 17, 29, 11, 17, 13, 5, 13, 7, 13

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 26 2021

Keywords

• nonn

Comments

a(n) >= 5 for n >= 2, since A014574(n) == 0 (mod 6).

a(n) = 5 if and only if A001359(n) is in A022004.

Examples

			a(5) = 7 because A014574(5) = 30 and 7 is the least prime p such that 30+p is prime.
		

Links

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

Crossrefs

Cf. A001359, A014574, A022004.

Programs

Maple

P:= {seq(ithprime(i),i=1..10^4)}:
A014574:= sort(convert(map(`+`,P,1) intersect map(`-`,P,1),list)):
f:= proc(n) local p,t;
   p:= 2;
   do
      p:= nextprime(p);
      if isprime(p+A014574[n]) then return p fi
   od
end proc:
map(f, [$1..nops(A014574)]);