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

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, 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, 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

Offset: 1

Author

Neil Fernandez, Apr 06 2017

Keywords

• nonn
• look

Comments

If n is not divisible by 3, a(n)<=1, as the only possible p is 3. - Robert Israel, Jul 20 2020

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A237885, A284919, A284928.

Programs

Maple

f:= proc(n) local p1,p2,t;
  t:= 0: p1:= 2:
  do
    p1:= nextprime(p1);
    if p1 > n then return t fi;
    if isprime(p1+2*n) and isprime(2*n-p1)  then
      t:= t+1
    fi
  od
end proc:
map(f, [$1..1000]); # Robert Israel, Jul 20 2020

Mathematica

For[i = 1, i < 1001, i++,
ee = 2*i;
a = 0;
For[j = 3, j < ee/2, j += 2,
  If[PrimeQ[j] == True && PrimeQ[ee - j] == True,
   If[PrimeQ[ee + j] == True, a += 1, a = a]]];
Print[ee, " ", a]]

Extensions

Definition corrected by Robert Israel, Jul 20 2020