A139048 a(n) is the number of primes p, p <= the n-th prime, where (p + (1/p)*Product_{k=1..n} prime(k)) is prime, where prime(k) is the k-th prime.

1, 2, 3, 4, 3, 4, 3, 2, 2, 5, 2, 4, 2, 2, 6, 2, 3, 4, 4, 3, 5, 1, 3, 3, 3, 2, 3, 3, 6, 2, 1, 0, 0, 1, 2, 6, 2, 3, 1, 7, 3, 1, 1, 2, 0, 1, 4, 4, 2, 4, 4, 0, 3, 3, 4, 1, 2, 4, 2, 2, 1, 2, 2, 2, 1, 3, 2, 1, 4, 3, 2, 3, 2, 3, 3, 4, 5, 2, 2, 5, 4, 2, 2, 1, 2, 2, 1, 5, 0, 2, 1, 2, 4, 2, 4, 4, 1, 5, 1, 1, 1, 3, 2, 1, 1

Offset

1,2

Comments

Sequence's terms were calculated by Jacques Tramu.

Variant of A083021. [R. J. Mathar, Nov 03 2008]

Links

Table of n, a(n) for n=1..105.

Example

For n = 5: 2 + 3*5*7*11 = 1157 = 13*89; 3 + 2*5*7*11 = 773 = prime; 5 + 2*3*7*11 = 467 = prime; 7 + 2*3*5*11 = 337 = prime; 11 + 2*3*5*7 = 221 = 13*17. So a(5) = 3.

Prog

(PARI) a(n) = my(prn = prod(k=1, n, prime(k))); sum(k=1, n, isprime(prime(k) + prn/prime(k))); \\ Michel Marcus, Mar 18 2018

Crossrefs

Cf. A002110.

Sequence in context: A106826 A259582 A377937 * A182101 A242289 A349229

Adjacent sequences: A139045 A139046 A139047 * A139049 A139050 A139051

Keyword

nonn

Author

Leroy Quet, Jun 01 2008

Status

approved