A087859 a(n) is the number of twin primes x-1,x+1 such that x=j*(p(n)#)/p(k), where 1 <= j < p(n+1) and 1 <= k <= n and p(k) doesn't divide j.

0, 1, 3, 7, 8, 10, 15, 13, 13, 15, 10, 12, 15, 15, 18, 13, 22, 15, 23, 19, 23, 16, 19, 16, 22, 13, 15, 20, 23, 14, 18, 27, 20, 20, 16, 25, 21, 25, 14, 27, 21, 25, 29, 19, 26, 21, 25, 27, 21, 19, 15, 16, 32, 17, 19, 19, 21, 17, 22, 23, 29, 24, 29, 29, 18, 25, 25

Offset

1,3

Comments

p(n) is the n-th prime; # denotes primorial (A002110).

a(n) seems to grow like 4*log(p(n)).

Links

Table of n, a(n) for n=1..67.

Example

a(3) = 3 because for (j,k) = (1,3),(2,3),(3,3), j*(5#)/p(k)+-1 are primes.

Prog

(PARI) a(n) = {my(p=vector(n, i, prime(i)), x, y=prod(i=1, n, p[i])); sum(j=1, prime(n+1)-1, sum(k=1, n, j%p[k]>0 && ispseudoprime(x=j*y/p[k]-1) && ispseudoprime(x+2))); } \\ Jinyuan Wang, Mar 20 2020

Crossrefs

Cf. A002110, A087941, A088968.

Sequence in context: A019270 A047357 A003607 * A300082 A050010 A316493

Adjacent sequences: A087856 A087857 A087858 * A087860 A087861 A087862

Keyword

nonn

Author

Pierre CAMI, Oct 25 2003

Extensions

Edited by Don Reble, Nov 16 2005

More terms from Jinyuan Wang, Mar 20 2020

Status

approved