A088968 a(n) is the number of consecutive primes x-3,x+3 such that x=j*(p(n)#/3)/p(k), where 1 <= j < p(n+1) and 3 <= k <= n and p(k) doesn't divide j.

0, 0, 0, 2, 3, 5, 6, 7, 13, 4, 10, 9, 2, 12, 8, 14, 6, 8, 16, 8, 9, 8, 19, 10, 15, 18, 17, 8, 10, 14, 9, 13, 10, 15, 14, 11, 15, 10, 13, 20, 15, 13, 14, 16, 16, 15, 19, 17, 14, 18, 13, 13, 15, 15, 7, 14, 16, 21, 12, 11, 13, 20, 7, 19, 18, 13, 8, 19

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

Jinyuan Wang, Table of n, a(n) for n = 1..100

Example

a(5) = 3 because for (j,k) = (1,3),(10,4),(8,5), j*(11#/3)/p(k)+-3 are consecutive primes.

Prog

(PARI) a(n) = {my(p=vector(n, i, prime(i)), x, y=2*prod(i=3, n, p[i])); sum(j=1, prime(n+1)-1, sum(k=3, n, j%p[k]>0 && ispseudoprime(x=j*y/p[k]-3) && nextprime(x+1)==x+6)); } \\ Jinyuan Wang, Mar 20 2020

Crossrefs

Cf. A002110, A087859, A087941.

Sequence in context: A362454 A046158 A070274 * A328451 A057924 A103538

Adjacent sequences: A088965 A088966 A088967 * A088969 A088970 A088971

Keyword

nonn

Author

Pierre CAMI, Oct 29 2003

Extensions

Edited by Don Reble, Nov 16 2005

Status

approved