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%I #23 Jun 14 2024 08:47:09
%S 1,2,5,11,35,103,323,1052,3469,11726,40234,139955,492505,1750900,
%T 6275491,22662455,82364564,301058002,1106006504,4081585024,
%U 15124027686,56247438994,209889216294,785601467368,2948682167318,11096081791175,41854378016484,158221313955249
%N 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.
%H Amiram Eldar, <a href="/A117758/b117758.txt">Table of n, a(n) for n = 0..39</a>
%e a(1) = 2 because the primes 3 and 5 lie in the interval (2,6].
%p 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
%t Do[Print[PrimePi[Binomial[2*n + 2, n + 1]] - PrimePi[Binomial[2*n, n]]], {n, 0, 25}] (* _Ryan Propper_, May 06 2006 *)
%o (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
%Y Cf. A000984, A036378.
%K nonn
%O 0,2
%A _Greg Huber_, Apr 14 2006
%E More terms from _Emeric Deutsch_ and _R. J. Mathar_, Apr 16 2006
%E More terms from _Ryan Propper_, May 06 2006
%E a(25)-a(27) from _Amiram Eldar_, Jun 14 2024
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