A135715 Number of primes of the form p(n)#/p(k) + 1, where 1 <= k <= n.

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

Offset

1,3

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 once, a(172)=8; the mode is 2, occurring 135 times.

Links

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

Example

a(3)=2 because p(3)#=A002110(3)=30 and 30/3+1=11 and 30/5+1=7 are both prime and there are no other primes of this form.

Mathematica

a[n_] := (p = Product[Prime[k], {k, 1, n}]; Sum[Boole[PrimeQ[p/Prime[k] + 1]], {k, 1, n}]); Array[a, 105] (* Jean-François Alcover, Nov 02 2017, translated from PARI *)

Prog

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

Crossrefs

Cf. A135714, A135716, A002110.

Sequence in context: A008968 A162499 A350857 * A089326 A359514 A237367

Adjacent sequences: A135712 A135713 A135714 * A135716 A135717 A135718

Keyword

nonn

Author

Rick L. Shepherd, Nov 30 2007

Status

approved