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A284950 Number of primes p <= n such that 2*n-p and 2*n+p are prime.

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