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, 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

Amiram Eldar, Table of n, a(n) for n = 0..39

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

Cf. A000984, A036378.

Sequence in context: A298122 A196690 A101834 * A284251 A343162 A353210

Adjacent sequences: A117755 A117756 A117757 * A117759 A117760 A117761

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