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A121069
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Conjectured sequence for jumping champions greater than 1 (most common prime gaps up to x, for some x).
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5
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2, 4, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070
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OFFSET
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1,1
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COMMENTS
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If n > 2, then a(n) = product of n-1 consecutive distinct prime divisors. E.g. a(5)=210, the product of 4 consecutive and distinct prime divisors, 2,3,5,7. - Enoch Haga, Dec 08 2007
Rather than have code merely generating the conjectured values, one can compare values of sequence terms at the same position n. Specifically, locate new maximums where (p,p+even) are both prime, where even=2,4,6,8,... and the datum set is taken with even=4. A new maximum implies a new jumping champion.
Doing this produces the terms 2,4,6,30,210,2310,30030,.... Looking at the plot of a(n) ratio for gap=2/gap=6, the value changes VERY slowly, and is 2.14 after 50 million terms (one can see the trend via Plot 2 of A001359 vs A023201 (3rd option seqA/seqB vs n). The ratio for gap=4/gap=2 ~ 1, implying they are equally frequent. (End)
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LINKS
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A. M. Odlyzko, M. Rubinstein, and M. Wolf, Jumping Champions, Experiment. Math. 8(2): 107-118 (1999).
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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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PROG
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CROSSREFS
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Cf. A087103, A087104, A001223, A000230, A001632, A038664, A086977-A086980, A085237, A005250, A053686, A054587, A093737-A093753, A093972-A093984.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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