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
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.
Programs
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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]);