A317595 a(n) is the number of primes between 2n and the largest prime p such that 2n-p is also a prime.

1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0

Offset

2,48

Comments

If the Goldbach Conjecture is true, this sequence is defined for n >= 2.

Links

Table of n, a(n) for n=2..88.

Index entries for sequences related to Goldbach conjecture

Formula

a(n) = A000720(A020482(n)) - A020482(2*n). - Michel Marcus, Aug 02 2018

Example

For n=2, 2n=4 = 2+2, there is one prime, which is 3, between 2 and 4. So a(2)=1;
...
For n=8, 2n=16 = 13+3, there is no prime between 13 and 16. So a(8)=0;
...
For n=49, 2n=98 = 79+19, there are three primes, 83, 89, and 97 between 79 and 98 such that the difference of 98 and these primes, 15, 9, and 1 respectively, are not prime. So a(49)=3.

Mathematica

Table[n2 = n*2; p = NextPrime[n2]; ct = 0; While[p = NextPrime[p, -1]; ! PrimeQ[n2 - p], ct++]; ct, {n, 2, 88}]

Crossrefs

Cf. A000040, A000720, A002375, A020482.

Sequence in context: A307808 A200472 A309887 * A263753 A303877 A112743

Adjacent sequences: A317592 A317593 A317594 * A317596 A317597 A317598

Keyword

nonn,easy

Author

Lei Zhou, Aug 01 2018

Status

approved