Search: id:A108954
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%I A108954
%S A108954 1,1,1,2,1,2,2,2,3,4,3,4,3,3,4,5,4,4,4,4,5,6,5,6,6,6,7,7,6,7,7,7,7,8,8,
%T A108954 9,9,9,9,10,9,10,9,9,10,10,9,9,10,10,11,12,11,12,13,13,14,14,13,13,12,
%U A108954 12,12,13,13,14,13,13,14,15,14,14,13,13,14,15,15,15,15,15,15,16,15,16
%N A108954 a(n) = Pi(2n) - Pi(n).
%C A108954 a(n) < log(4)*n/log(n) < 7*n/(5*log(n)) for n > 1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Mar 04 2008
%C A108954 Bertrand's postulate is equivalent to the formula a(n) => 1 for all positive 
               integers n. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 30 
               2008
%D A108954 F. Irschebeck, Einladung zur Zahlentheorie, BI Wissenschaftsverlag 1992, 
               p. 40
%H A108954 T. D. Noe, <a href="b108954.txt">Table of n, a(n) for n=1..1000</a>
%H A108954 Tsutomu Hashimoto, <a href="http://arxiv.org/abs/0807.3690">On a certain 
               relation between Legendre's conjecture and Bertrand's postulate</
               a>
%F A108954 Pi(x) = number of prime numbers less than or equal to x.
%F A108954 For n > 1, a(n) = A060715(n). - David Wasserman (wasserma(AT)spawar.navy.mil), 
               Nov 04 2005
%o A108954 (PARI) g(n) = for(x=1,n,y=primepi(2*x)-primepi(x);print1(y","))
%Y A108954 a(n)=A000720(2*n)-A000720(n).
%Y A108954 Cf. A000720, A060715.
%Y A108954 Sequence in context: A114920 A030361 A060715 this_sequence A123920 A029170 
               A079526
%Y A108954 Adjacent sequences: A108951 A108952 A108953 this_sequence A108955 A108956 
               A108957
%K A108954 easy,nonn
%O A108954 1,4
%A A108954 Cino Hilliard (hillcino368(AT)gmail.com), Jul 22 2005

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