A087941 a(n) is the number of consecutive primes x-2,x+2 such that x=j*(p(n)#/2)/p(k), where 1 <= j < p(n+1) and 2 <= k <= n and p(k) doesn't divide j.

0, 0, 1, 3, 7, 4, 4, 6, 7, 9, 7, 8, 8, 6, 9, 9, 7, 7, 6, 10, 9, 10, 5, 9, 10, 5, 8, 10, 13, 8, 15, 7, 6, 13, 8, 7, 8, 14, 13, 13, 11, 11, 7, 11, 10, 8, 11, 5, 11, 12, 14, 6, 16, 14, 15, 15, 12, 9, 7, 7, 13, 11, 10, 12, 12, 10, 13, 11, 7, 14, 14, 13, 14, 10, 13

Offset

1,4

Comments

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

a(n) seems to grow like 2*log(p(n)).

Links

Table of n, a(n) for n=1..75.

Example

a(4) = 3 because for (j,k) = (1,3),(1,4),(3,4), j*(7#/2)/p(k)+-2 are consecutive primes.

Prog

(PARI) a(n) = {my(p=vector(n, i, prime(i)), x, y=prod(i=2, n, p[i])); sum(j=1, prime(n+1)-1, sum(k=2, n, j%p[k]>0 && ispseudoprime(x=j*y/p[k]-2) && nextprime(x+1)==x+4)); } \\ Jinyuan Wang, Mar 20 2020

Crossrefs

Cf. A002110, A087859, A088968.

Sequence in context: A256676 A349010 A267412 * A278389 A021271 A238274

Adjacent sequences: A087938 A087939 A087940 * A087942 A087943 A087944

Keyword

nonn

Author

Pierre CAMI, Oct 27 2003

Extensions

Edited by Don Reble, Nov 16 2005

More terms from Jinyuan Wang, Mar 20 2020

Status

approved