1,1

a(n) = product of n consecutive distinct prime divisors. E.g. a(4)=210, the product of 4 consecutive and distinct prime divisors, 2,3,5,7. - Enoch Haga (Enokh(AT)comcast.net), Dec 08 2007

In 1999 A. Odlyzko, M. Rubinstein, and M. Wolf formulated, on the basis of heuristic and empirical evidence, the conjecture that the numbers greater than 1 that are jumping champions are 4 and the sequence of primorials 2, 6, 30, 210, 2310, .... The authors pointed out that this conjecture is not a direct consequence of other deep conjectures concerning primes. Therefore they made a weaker and possibly more accessible conjecture, that any fixed prime p divides all sufficiently large jumping champions. In the present paper we shall extend the work of P. Erdos and E. G. Straus from 1980 to prove that this second conjecture follows directly from the prime pair conjecture of G. H. Hardy and J. E. Littlewood. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 17 2009]

I. Stewart, "Jumping Champions" in 'Scientific American' pp. 80-1 December 2000.

R. P. Brent, The First Occurence of Large Gaps Between Successive Primes

R. P. Brent, The distribution of small gaps between successive primes

R. P. Brent, The first occurrence of certain large prime gaps

C. K. Caldwell, The Prime Glossary, gaps between primes

C. K. Caldwell, The Prime Glossary, Jumping champion

A. M. Odlyzko, M. Rubinstein & M. Wolf, Jumping Champions

A. M. Odlyzko, M. Rubinstein & M. Wolf, Jumping Champions

A. M. Odlyzko, M. Rubinstein & M. Wolf, CHANCE News 10.02, 10. Jumping champions in the world of primes

A. M. Odlyzko, M. Rubinstein and M. Wolf, Jumping Champions

O. e Silva, Gaps between consecutive primes

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics

I. Stewart, Jumping Champions

D. A. Goldston, A. H. Ledoan, Jumping champions and gaps between consecutive primes, Oct 15, 2009. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 17 2009]

Consists of 4 and the primorials (A002110).

a(1) = 2, a(2) = 4, a(3) = 6, a(n+1)/a(n) = Prime[n] for n>2.

2, 4, Table[Product[Prime[k], {k, 1, n-1}], {n, 3, 30}]

Cf. A087103; A087104.

Cf. A001223, A000230, A001632, A038664, A086977-A086980, A085237, A005250, A053686, A054587, A093737-A093753, A093972-A093984.

Sequence in context: A077633 A006933 A046847 this_sequence A100838 A056696 A045662

Adjacent sequences: A121066 A121067 A121068 this_sequence A121070 A121071 A121072

nonn

Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 10 2006

Corrected and extended by Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 11 2006