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Search: id:A050216
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| A050216 |
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Number of primes between (prime(n))^2 and (prime(n+1))^2, with a(0) = 2 by convention. |
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4
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| 2, 2, 5, 6, 15, 9, 22, 11, 27, 47, 16, 57, 44, 20, 46, 80, 78, 32, 90, 66, 30, 106, 75, 114, 163, 89, 42, 87, 42, 100, 354, 99, 165, 49, 299, 58, 182, 186, 128, 198, 195, 76, 356, 77, 144, 75, 463, 479, 168, 82, 166, 270, 90, 438, 275, 274, 292, 91, 292, 199, 99
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The function in Brocard's Conjecture.
The lines in the graph correspond to prime gaps of 2, 4, 6,... - T. D. Noe, Feb 04 2008
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
Eric Weisstein's World of Mathematics, Brocard's Conjecture
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EXAMPLE
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There are 2 primes less than 2^2, there are 2 primes between 2^2 and 3^2, 5 primes between 5^2 and 7^2, etc.
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MATHEMATICA
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PrimePi[ Prime[ n+1 ]^2 ]-PrimePi[ Prime[ n ]^2 ]
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CROSSREFS
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First differences of A000879. Cf. A089609.
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KEYWORD
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nonn,new
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Edited by njas, Nov 15 2009
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