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

Author

Lekraj Beedassy, Mar 11 2002

Keywords

• hard
• more
• nonn

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

• 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.

Crossrefs

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

Programs

Mathematica

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

Formula

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

Extensions

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

a(13) from Donovan Johnson, Dec 08 2009