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

1,12

Comments

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

Links

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

Example

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.

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]]

Crossrefs

Cf. A237885, A284919, A284928.

Sequence in context: A187616 A217262 A260616 * A308298 A364106 A364033

Adjacent sequences: A284947 A284948 A284949 * A284951 A284952 A284953

Keyword

nonn,look

Author

Neil Fernandez, Apr 06 2017

Extensions

Definition corrected by Robert Israel, Jul 20 2020

Status

approved