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A117758
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.
1
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, 11096081791175, 41854378016484, 158221313955249
OFFSET
0,2
LINKS
EXAMPLE
a(1) = 2 because the primes 3 and 5 lie in the interval (2,6].
MAPLE
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, Apr 16 2006
MATHEMATICA
Do[Print[PrimePi[Binomial[2*n + 2, n + 1]] - PrimePi[Binomial[2*n, n]]], {n, 0, 25}] (* Ryan Propper, May 06 2006 *)
PROG
(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, Apr 21 2006
CROSSREFS
Sequence in context: A298122 A196690 A101834 * A284251 A343162 A353210
KEYWORD
nonn
AUTHOR
Greg Huber, Apr 14 2006
EXTENSIONS
More terms from Emeric Deutsch and R. J. Mathar, Apr 16 2006
More terms from Ryan Propper, May 06 2006
a(25)-a(27) from Amiram Eldar, Jun 14 2024
STATUS
approved