A083021 a(n) = the number of distinct primes of the form p(n)#/p(i) + p(i).

1, 1, 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

1,3

Comments

Some of the larger entries may only correspond to probable primes.

Links

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

Example

p(n) is the n-th prime; # denotes primorial (A002110).
a(2)=1 because 3#/2+2 and 3#/3+3 are the same prime (5).
a(4)=4 because 7#/2+2=107, 7#/3+3=73, 7#/5+5=47, 7#/7+7=37 are four primes.

Prog

(PARI) p_n_primorial(n) = { prod(i=1, n, prime(i)) }
a(n) = { my(p=p_n_primorial(n), c=0); if(n==2, 1, for(i=1, n, my(q=p/prime(i)+prime(i)); if(isprime(q), c++)); c) }

Crossrefs

Cf. A002110.

Sequence in context: A270827 A293072 A120447 * A102745 A108026 A010702

Adjacent sequences: A083018 A083019 A083020 * A083022 A083023 A083024

Keyword

nonn

Author

Rick L. Shepherd, May 31 2003

Extensions

Edited by Don Reble, Nov 16 2005

Status

approved