cp's OEIS Frontend

A075699 Number of primes in the interval (n,4n].

%I A075699 #27 Sep 06 2024 12:40:34
%S A075699 2,3,3,4,5,6,5,7,7,8,9,10,9,10,11,12,12,13,13,14,15,15,15,15,16,18,19,
%T A075699 20,20,20,19,20,21,21,23,23,22,24,24,25,25,26,25,26,27,28,27,28,29,31,
%U A075699 31,31,31,31,31,32,33,34,34,35,35,35,36,36,37,38,37,39,39,40,41,41,40
%N A075699 Number of primes in the interval (n,4n].
%C A075699 Difference a(n+1) - a(n) = -1, 0, 1, 2, ... .
%H A075699 Amiram Eldar, <a href="/A075699/b075699.txt">Table of n, a(n) for n = 1..10000</a>
%H A075699 Madhuparna Das and Goutam Paul, <a href="https://arxiv.org/abs/1710.09891">Revisiting Generalized Bertand's Postulate and Prime Gaps</a>, arXiv:1710.09891 [math.NT], 2017-2019.
%F A075699 a(n) = A000720(4n) - A000720(n). - _Michel Marcus_, Oct 02 2013
%e A075699 a(4) = 4 because between 4 and 16 there are 4 primes: 5, 7, 11, 13.
%e A075699 a(7) = 5 because between 7 and 28 there are 5 primes: 11, 13, 17, 19, 23.
%p A075699 A075699 := proc(n)
%p A075699     numtheory[pi](4*n)-numtheory[pi](n) ;
%p A075699 end proc: # _R. J. Mathar_, Nov 03 2017
%t A075699 s=4; a[n_] := PrimePi[s*n]-PrimePi[n]
%o A075699 (PARI) a(n) = primepi(4*n) - primepi(n); \\ _Michel Marcus_, Oct 02 2013
%Y A075699 Cf. A000720, A074990, A108954.
%K A075699 nonn
%O A075699 1,1
%A A075699 _Zak Seidov_, Oct 02 2002