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A121069 Conjectured sequence for jumping champions (most common prime gaps). +0
5
2, 4, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070 (list; graph; listen)
OFFSET

1,1

COMMENT

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

REFERENCES

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

LINKS

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

FORMULA

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.

MATHEMATICA

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

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

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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