Search: id:A060715
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%I A060715
%S A060715 0,1,1,2,1,2,2,2,3,4,3,4,3,3,4,5,4,4,4,4,5,6,5,6,6,6,7,7,6,7,7,7,7,8,8,
%T A060715 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 A060715 12,12,13,13,14,13,13,14,15,14,14,13,13,14,15,15,15,15,15,15,16,15,16
%N A060715 Number of primes between n and 2n exclusive.
%C A060715 See the additional references and links mentioned in A143227. [From Jonathan 
               Sondow (jsondow(AT)alumni.princeton.edu), Aug 03 2008]
%D A060715 M. Aigner and C. M. Ziegler, Proofs from The Book, Chapter 2, Springer 
               NY 2001.
%H A060715 T. D. Noe, <a href="b060715.txt">Table of n, a(n) for n=1..1000</a>
%H A060715 Math Olympiads, <a href="http://matholymp.com/TUTORIALS/Bertrand.pdf">
               Bertrand's Postulate</a>
%H A060715 R. Chapman, <a href="http://www.maths.ex.ac.uk/~rjc/etc/bertrand.pdf">
               Bertrand postulate</a>
%H A060715 S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/
               Cpaper24/page1.htm">A Proof Of Bertrand's Postulate</a>
%H A060715 M. Slone, PlanetMath.org, <a href="http://planetmath.org/encyclopedia/
               ProofOfBertrandsConjecture.html">Proof of Bertrand's conjecture</
               a>
%H A060715 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BertrandsPostulate.html">Link to a section of The World of Mathematics.</
               a>
%H A060715 Wolfram Research, <a href="http://functions.wolfram.com/NumberTheoryFunctions/
               Prime/31/03/ShowAll.html">Bertrand hypothesis</a>
%H A060715 Wikipedia, <a href="http://en.wikipedia.org/wiki/Proof_of_Bertrand%27s_postulate">
               Proof of Bertrand's postulate</a>
%H A060715 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php/Bertrandspostulate.html">Bertrand's postulate</a>
%H A060715 Dr. Wilkinson, The Math Forum, <a href="http://mathforum.org/library/
               drmath/view/51527.html">Erdos' Proof</a>
%e A060715 a(35)=8 since eight consecutive primes (37,41,43,47,53,59,61,67) are 
               located between 35 and 70.
%p A060715 a := proc(n) local counter, i; counter := 0; from i from n+1 to 2*n-1 
               do if isprime(i) then counter := counter +1; fi; od; return counter; 
               end:
%o A060715 (PARI) { for (n=1, 1000, write("b060715.txt", n, " ", primepi(2*n - 1) 
               - primepi(n)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jul 10 2009]
%Y A060715 Cf. A060756, A070046, A006992, A051501, A035250.
%Y A060715 Cf. A101909
%Y A060715 Cf. A000720, A014085, A104272, A143223, A143224, A143225, A143226, A143227. 
               [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 03 2008]
%Y A060715 Sequence in context: A123505 A114920 A030361 this_sequence A108954 A123920 
               A029170
%Y A060715 Adjacent sequences: A060712 A060713 A060714 this_sequence A060716 A060717 
               A060718
%K A060715 nonn,easy
%O A060715 1,4
%A A060715 Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 25 2001
%E A060715 Corrected by Dug Eichelberger (dug(AT)mit.edu), Jun 04 2001. More terms 
               from Larry Reeves (larryr(AT)acm.org), Jun 05 2001

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