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Search: id:A121069
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| A121069 |
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Conjectured sequence for jumping champions (most common prime gaps). |
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+0
5
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| 2, 4, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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REFERENCES
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I. Stewart, "Jumping Champions" in 'Scientific American' pp. 80-1 December 2000.
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LINKS
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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
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FORMULA
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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.
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MATHEMATICA
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2, 4, Table[Product[Prime[k], {k, 1, n-1}], {n, 3, 30}]
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 10 2006
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EXTENSIONS
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Corrected and extended by Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 11 2006
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