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Search: id:A117758
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| A117758 |
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Number of primes between the successive central binomial coefficients; i.e. the number of primes in the interval (C(2n,n),C(2n+2,n+1)], with inclusion on the right. |
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+0
1
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| 1, 2, 5, 11, 35, 103, 323, 1052, 3469, 11726, 40234, 139955, 492505, 1750900, 6275491, 22662455, 82364564, 301058002, 1106006504, 4081585024, 15124027686, 56247438994, 209889216294, 785601467368, 2948682167318
(list; graph; listen)
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OFFSET
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0,2
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EXAMPLE
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a(1) = 2 because the primes 3 and 5 lie in the interval (2,6].
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MAPLE
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a:=proc(n) local ct, j: ct:=0: for j from binomial(2*n, n)+1 to binomial(2*n+2, n+1) do if isprime(j)=true then ct:=ct+1 else fi: ct: od: end: seq(a(n), n=0..13); # execution takes hours - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 16 2006
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MATHEMATICA
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Do[Print[PrimePi[Binomial[2*n + 2, n + 1]] - PrimePi[Binomial[2*n, n]]], {n, 0, 25}] - Ryan Propper (rpropper(AT)stanford.edu), May 06 2006
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PROGRAM
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(PARI) { for(n=0, 30, istrt=binomial(2*n, n) ; iend=binomial(2*n+2, n+1) ; resul=0 ; forprime(p=istrt+1, iend, resul++ ; ) ; print1(resul, ", ") ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 21 2006
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CROSSREFS
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Cf. A036378.
Sequence in context: A006400 A080068 A101834 this_sequence A130622 A112600 A092298
Adjacent sequences: A117755 A117756 A117757 this_sequence A117759 A117760 A117761
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KEYWORD
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nonn
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AUTHOR
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Greg Huber (huber(AT)alum.mit.edu), Apr 14 2006
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2006
More terms from Ryan Propper (rpropper(AT)stanford.edu), May 06 2006
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