

A305866


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


1



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
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OFFSET

1,4


LINKS

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


EXAMPLE

For n=1, p(n)=2, 2+2+1=5 is prime. So a(1)=1;
For n=2, p(n)=3, 3+2+1=6 is not prime, 3+3+1=7 is prime. So a(2)=1;
...
For n=5, p(5)=11, 11+5+1=17, 11+7+1=19, 11+11+1=23. Three 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 * A328406 A257396 A293519
Adjacent sequences: A305863 A305864 A305865 * A305867 A305868 A305869


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Jun 12 2018


STATUS

approved



