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A200474
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a(n) = floor(10*(prime(n+1)-prime(n))/log(prime(n))^2).
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2
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3, 6, 2, 4, 6, 1, 5, 3, 1, 2, 4, 3, 1, 3, 2, 1, 3, 2, 3, 3, 1, 0, 1, 0, 1, 6, 1, 2, 0, 4, 0, 2, 2, 1, 2, 2, 0, 3, 0, 1, 0, 4, 4, 1, 0, 1, 2, 0, 3, 1, 1, 1, 0, 1, 1, 0, 3, 4, 1, 0, 1, 4, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 0, 1, 1, 1, 2, 1, 0, 1, 3
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OFFSET
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5,1
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COMMENTS
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Cramer's conjecture is true if, for every n >= 5, a(n) is smaller than 10.
If Cramer's conjecture is true, then Andrica's conjecture is true. [John W. Nicholson, Feb 06 2012]
Some mathematicians are trying to prove: if Andrica's conjecture is true, then Cramer's conjecture is true. [Arkadiusz Wesolowski, Feb 22 2012]
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LINKS
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FORMULA
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EXAMPLE
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a(9) = 6 because 10*(29-23)/log(23)^2 = 6.1029419977....
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MATHEMATICA
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Table[Floor[10*(Prime[n + 1] - Prime[n])/Log[Prime[n]]^2], {n, 5, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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