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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.

%I A381062 #5 Feb 13 2025 10:00:46
%S A381062 2,19,9733,69398759
%N 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.
%e A381062 a(2) = 19 because the sum of any 3 of the 4 primes 19, 23, 29, 31 is prime:
%e A381062   19 + 23 + 29 = 71
%e A381062   19 + 23 + 31 = 73
%e A381062   19 + 29 + 31 = 79
%e A381062   23 + 29 + 31 = 83 are all prime, and 19 is the first prime that works.
%p A381062 f:= proc(n) local P,S,p,i;
%p A381062   P:= [0,seq(ithprime(i),i=1..2*n-1)]:
%p A381062   S:= convert(P,`+`);
%p A381062   do
%p A381062     p:= nextprime(P[-1]);
%p A381062     S:= S + p - P[1];
%p A381062     P:= [op(P[2..-1]),p];
%p A381062     if andmap(t -> isprime(S-t),P) then return P[1] fi
%p A381062   od
%p A381062 end proc:
%p A381062 map(f, [$1..4]);
%Y A381062 Cf. A298763, A381061.
%K A381062 nonn,more
%O A381062 1,1
%A A381062 _Robert Israel_, Feb 12 2025