A317595 - OEIS

%I #16 Aug 11 2018 20:40:02

%S 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,

%T 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,

%U 1,0,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0

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

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

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%F a(n) = A000720(A020482(n)) - A020482(2*n). - _Michel Marcus_, Aug 02 2018

%e For n=2, 2n=4 = 2+2, there is one prime, which is 3, between 2 and 4. So a(2)=1;

%e ...

%e For n=8, 2n=16 = 13+3, there is no prime between 13 and 16. So a(8)=0;

%e ...

%e 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.

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

%Y Cf. A000040, A000720, A002375, A020482.

%K nonn,easy

%O 2,48

%A _Lei Zhou_, Aug 01 2018