A068489 m for which prime(m) is the least prime dividing #prime(n) - 1, i.e., one less than primorial n-th prime (A057588).

3, 10, 5, 343, 3248, 18, 16, 12, 22, 20324, 50, 9414916809095, 13120, 43, 8481, 1200361259, 196, 38, 10326732314, 65, 38, 34

Offset

2,1

Comments

Since #P13 - 1 is a prime, see A006794, we need the number of primes less than or equal to #P13 - 1. The sequence continues, for n=14 to 23: 13120, 43, 8481, 1200361259, 196, 38, 10326732314, 65, 38, 34.

a(24) = pi(23768741896345550770650537601358309). - Donovan Johnson, Dec 08 2009

Links

Table of n, a(n) for n=2..23.

Romeo Meštrović, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023. - From N. J. A. Sloane, Jun 13 2012

Hisanori Mishima, Factorization results #Pn (Primorial) - 1.

Formula

a(n) = A000720(A057713(n)).

Mathematica

Do[ Print[ PrimePi[ FactorInteger[ Product[ Prime[k], {k, 1, n}] - 1] [[1, 1]]]], {n, 2, 22} ]

Crossrefs

Cf. A000720, A006794, A057588, A057713, A068488.

Sequence in context: A280529 A281279 A367322 * A088337 A195919 A275741

Adjacent sequences: A068486 A068487 A068488 * A068490 A068491 A068492

Keyword

hard,more,nonn

Author

Lekraj Beedassy, Mar 11 2002

Extensions

Edited and extended by Robert G. Wilson v, Mar 12 2002

a(13) from Donovan Johnson, Dec 08 2009

Status

approved