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A058077
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Binomial coefficients formed from consecutive primes: a(n) = binomial( prime(n+1), prime(n) ).
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15
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3, 10, 21, 330, 78, 2380, 171, 8855, 475020, 465, 2324784, 101270, 903, 178365, 22957480, 45057474, 1830, 99795696, 971635, 2628, 277962685, 1837620, 581106988, 144520208820, 4082925, 5253, 5160610, 5886, 6438740
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OFFSET
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1,1
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COMMENTS
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Conjecture: for each value of n > 1, if a(n+1) has the same number of digits as a(n) and a(n+1) > a(n), then prime(n+2) - prime(n+1) = prime(n+1) - prime(n). This conjecture has been verified for all n < 3*10^7. - Ahmad J. Masad, Oct 08 2019
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LINKS
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FORMULA
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EXAMPLE
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n=6: a(6) = C(p(7),p(6)) = C(17,13) = 57120/24 = 2380.
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MATHEMATICA
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Table[Binomial[Prime[n+1], Prime[n]], {n, 1, 20}] (* Vaclav Kotesovec, Nov 13 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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