A135714 Number of primes of the form p(n)#/p(k) - 1, where 1 <= k <= n.

0, 1, 1, 2, 2, 4, 2, 3, 4, 1, 0, 3, 3, 3, 3, 5, 2, 0, 3, 3, 5, 2, 2, 1, 5, 4, 2, 1, 2, 0, 0, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 3, 0, 3, 4, 0, 4, 1, 0, 1, 3, 0, 2, 2, 5, 1, 2, 1, 5, 1, 1, 2, 1, 1, 3, 6, 3, 2, 4, 4, 0, 1, 2, 2, 4, 1, 4, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 4, 2, 2, 0, 4, 3, 2, 2, 4, 1, 0, 0, 2, 2, 3, 4, 4, 3

Offset

1,4

Comments

p(k) is k-th prime; p(n)# is n-th primorial, A002110(n). For the larger n, these are only counts of highly probable primes. Of the first 500 terms, the maximum occurs twice, a(366)=a(432)=7; the mode is 2, occurring 142 times.

Links

Rick Shepherd, Table of n, a(n) for n = 1..500

Example

a(6)=4 because p(6)#=A002110(6)=30030 and 30030/3-1=10009, 30030/7-1=4289, 30030/11-1=2729 and 30030/13-1=2309 are all prime and there are no other primes of this form.

Prog

(PARI) a(n)= p=prod(k=1, n, prime(k)); sum(k=1, n, isprime(p/prime(k)-1))

Crossrefs

Cf. A135715, A135716, A002110.

Sequence in context: A057939 A163371 A061338 * A103274 A046820 A356878

Adjacent sequences: A135711 A135712 A135713 * A135715 A135716 A135717

Keyword

nonn

Author

Rick L. Shepherd, Nov 28 2007

Status

approved