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%I #15 Jul 21 2020 06:02:23
%S 0,0,0,1,1,1,1,1,1,1,0,2,1,0,3,0,1,3,0,1,3,1,0,3,1,0,3,1,0,5,0,1,4,0,
%T 1,3,0,1,4,0,0,4,1,0,6,0,0,4,0,1,2,1,1,4,1,0,4,0,0,9,0,0,5,0,0,5,1,0,
%U 4,0,0,5,0,0,6,0,1,5,0,1,5,0,0,7,1,0,5,1,0,7,0,0,6,0,0,4,1,1,4,0
%N Number of primes p <= n such that 2*n-p and 2*n+p are prime.
%C If n is not divisible by 3, a(n)<=1, as the only possible p is 3. - _Robert Israel_, Jul 20 2020
%H Robert Israel, <a href="/A284950/b284950.txt">Table of n, a(n) for n = 1..10000</a>
%e a(5) is 1, because of all the pairs of primes p1 <= p2 which sum to 5*2=10, namely {3,7} and {5,5}, only (3,7) has p1+10 prime.
%p f:= proc(n) local p1,p2,t;
%p t:= 0: p1:= 2:
%p do
%p p1:= nextprime(p1);
%p if p1 > n then return t fi;
%p if isprime(p1+2*n) and isprime(2*n-p1) then
%p t:= t+1
%p fi
%p od
%p end proc:
%p map(f, [$1..1000]); # _Robert Israel_, Jul 20 2020
%t For[i = 1, i < 1001, i++,
%t ee = 2*i;
%t a = 0;
%t For[j = 3, j < ee/2, j += 2,
%t If[PrimeQ[j] == True && PrimeQ[ee - j] == True,
%t If[PrimeQ[ee + j] == True, a += 1, a = a]]];
%t Print[ee, " ", a]]
%Y Cf. A237885, A284919, A284928.
%K nonn,look
%O 1,12
%A _Neil Fernandez_, Apr 06 2017
%E Definition corrected by _Robert Israel_, Jul 20 2020
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