A305866 a(n) is the number of primes that are equal to prime(n)+q+1, where prime(n) is the n-th prime number, q is a prime less than or equal to prime(n).

1, 1, 1, 2, 3, 2, 3, 3, 6, 6, 3, 4, 8, 4, 7, 9, 11, 5, 6, 9, 4, 7, 13, 15, 8, 11, 7, 13, 10, 13, 9, 16, 15, 12, 19, 9, 8, 8, 20, 20, 25, 11, 17, 11, 18, 15, 9, 13, 21, 14, 25, 28, 11, 27, 24, 26, 32, 13, 12, 22, 14, 29, 19, 27, 14, 26, 14, 14, 29, 24, 26, 40

Offset

1,4

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

Example

For n=1, prime(n)=2, 2+2+1=5 is prime. So a(1)=1;
For n=2, prime(n)=3, 3+2+1=6 is not prime, 3+3+1=7 is prime. So a(2)=1;
...
For n=5, prime(5)=11, 11+5+1=17, 11+7+1=19, 11+11+1=23: 3 primes found. So a(5)=3.

Mathematica

Table[ct = 0; p = Prime[i]; Do[q = Prime[j]; If[PrimeQ[p + q + 1], ct++], {j, 1, i}]; ct, {i, 1, 72}]

Prog

(PARI) a(n) = sum(k=1, n, isprime(prime(n) + prime(k)+1)); \\ Michel Marcus, Jun 12 2018

Crossrefs

Cf. A000040.

Sequence in context: A032154 A300651 A003051 * A346708 A328406 A257396

Adjacent sequences: A305863 A305864 A305865 * A305867 A305868 A305869

Keyword

nonn,easy

Author

Lei Zhou, Jun 12 2018

Status

approved