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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 19 13:29 EDT 2024. Contains 376012 sequences. (Running on oeis4.)