A381062 a(n) is the first prime p such that the sum of any 2*n-1 of the 2*n consecutive primes starting with p is prime.

2, 19, 9733, 69398759

Offset: 1

Author

Robert Israel, Feb 12 2025

Keywords

• nonn
• more

Examples

			a(2) = 19 because the sum of any 3 of the 4 primes 19, 23, 29, 31 is prime:
  19 + 23 + 29 = 71
  19 + 23 + 31 = 73
  19 + 29 + 31 = 79
  23 + 29 + 31 = 83 are all prime, and 19 is the first prime that works.
		

Crossrefs

Cf. A298763, A381061.

Programs

Maple

f:= proc(n) local P,S,p,i;
  P:= [0,seq(ithprime(i),i=1..2*n-1)]:
  S:= convert(P,`+`);
  do
    p:= nextprime(P[-1]);
    S:= S + p - P[1];
    P:= [op(P[2..-1]),p];
    if andmap(t -> isprime(S-t),P) then return P[1] fi
  od
end proc:
map(f, [$1..4]);