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Search: id:A060715
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| A060715 |
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Number of primes between n and 2n exclusive. |
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+0
30
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| 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, 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, 12, 12, 13, 13, 14, 13, 13, 14, 15, 14, 14, 13, 13, 14, 15, 15, 15, 15, 15, 15, 16, 15, 16
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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See the additional references and links mentioned in A143227. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 03 2008]
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REFERENCES
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M. Aigner and C. M. Ziegler, Proofs from The Book, Chapter 2, Springer NY 2001.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Math Olympiads, Bertrand's Postulate
R. Chapman, Bertrand postulate
S. Ramanujan, A Proof Of Bertrand's Postulate
M. Slone, PlanetMath.org, Proof of Bertrand's conjecture
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wolfram Research, Bertrand hypothesis
Wikipedia, Proof of Bertrand's postulate
C. K. Caldwell, The Prime Glossary, Bertrand's postulate
Dr. Wilkinson, The Math Forum, Erdos' Proof
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EXAMPLE
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a(35)=8 since eight consecutive primes (37,41,43,47,53,59,61,67) are located between 35 and 70.
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MAPLE
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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:
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PROGRAM
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(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]
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CROSSREFS
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Cf. A060756, A070046, A006992, A051501, A035250.
Cf. A101909
Cf. A000720, A014085, A104272, A143223, A143224, A143225, A143226, A143227. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 03 2008]
Sequence in context: A123505 A114920 A030361 this_sequence A108954 A123920 A029170
Adjacent sequences: A060712 A060713 A060714 this_sequence A060716 A060717 A060718
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KEYWORD
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nonn,easy
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 25 2001
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EXTENSIONS
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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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