%I #12 May 16 2023 10:39:54
%S 0,1,1,3,1,3,3,4,3,2,4,6,4,4,4,5,2,6,7,4,7,7,6,6,8,5,8,6,7,7,8,6,8,9,
%T 7,10,11,8,8,9,8,9,8,10,7,9,11,14,10,13,11,9,12,13,10,12,12,13,12,10,
%U 15,15,17,15,12,12,12,15,15,17,17,11,16,16,17,17,13,19,14,17,14,17,12,15,19
%N a(n) is the number of primes of the form prime(n) + 2*q where q < prime(n) is prime.
%H Robert Israel, <a href="/A344793/b344793.txt">Table of n, a(n) for n = 1..5000</a>
%e a(6) = 3 because with prime(6) = 13 we have 2*2+13 = 17, 2*3+13 = 19 and 2*5+13 = 23 prime.
%p f:= proc(n) local i,p;
%p p:= ithprime(n);
%p numboccur(true,map(isprime, [seq(2*ithprime(i)+p,i=1..n-1)]))
%p end proc:
%p map(f, [$1..100]);
%t a[n_] := Module[{p, q},
%t p = Prime[n];
%t q = Select[Range[p-1], PrimeQ];
%t Count[p + 2 q, _?PrimeQ]];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, May 16 2023 *)
%Y Cf. A344794.
%K nonn
%O 1,4
%A _J. M. Bergot_ and _Robert Israel_, May 28 2021