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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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6
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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
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OFFSET
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0,1
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COMMENTS
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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
Lengths of blocks of consecutive primes in A000430 (union of primes and squares of primes). [Reinhard Zumkeller, Sep 23 2011]
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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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PROG
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(Haskell)
import Data.List (group)
a050216 n = a050216_list !! (n-1)
a050216_list =
map length $ filter (/= [0]) $ group $ map a010051 a000430_list
-- Reinhard Zumkeller, Sep 23 2011
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CROSSREFS
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First differences of A000879. Cf. A089609.
Cf. A010051, A001248.
Sequence in context: A147766 A034420 A028410 * A080880 A120843 A205674
Adjacent sequences: A050213 A050214 A050215 * A050217 A050218 A050219
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Edited by N. J. A. Sloane, Nov 15 2009
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STATUS
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approved
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