%I #29 Oct 22 2024 02:55:56

%S 0,0,0,1,1,1,1,2,2,3,3,3,3,3,3,4,4,4,3,4,4,5,5,5,6,6,6,7,6,6,6,7,7,7,

%T 8,8,8,9,9,9,9,9,9,9,9,10,9,9,9,10,10,11,11,11,12,13,13,14,13,13,12,

%U 12,12,12,13,13,13,13,13,14,14,14,13,13,13,14,15,15,14,15,15,15,15,15

%N Number of primes p such that n < p < 2n-2.

%C a(n) > 0 for n > 3 by Bertrand's postulate (and Chebyshev's proof of 1852). - _Jonathan Vos Post_, Aug 08 2013

%H J. Sondow and E. Weisstein, <a href="http://mathworld.wolfram.com/BertrandsPostulate.html">Bertrand's Postulate</a>, World of Mathematics

%H M. Tchebichef, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k163969/f374.image.r=periodiques.langFR">Memoire sur les nombres premiers</a>, J. Math. Pures Appliq. 17 (1852) 366.

%e a(19) = 3, the first value smaller than a previous value, because the only primes between 19 and 2 * 19 - 2 = 36 are {23,29,31}. - _Jonathan Vos Post_, Aug 08 2013

%t a[n_] := PrimePi[2n - 2] - PrimePi[n]; a[1] = 0; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Oct 31 2012 *)

%Y Related sequences:

%Y Primes (p) and composites (c): A000040, A002808, A000720, A065855.

%Y Primes between p(n) and 2*p(n): A063124, A070046; between c(n) and 2*c(n): A376761; between n and 2*n: A035250, A060715, A077463, A108954.

%Y Composites between p(n) and 2*p(n): A246514; between c(n) and 2*c(n): A376760; between n and 2*n: A075084, A307912, A307989, A376759.

%K nonn

%O 1,8

%A _Eric W. Weisstein_, Nov 05 2002