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Search: id:A007918
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| A007918 |
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Least prime >= n (version 1 of the "next prime" function). |
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53
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| 2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, 19, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 59, 59, 59, 59, 61, 61, 67, 67, 67, 67, 67, 67, 71, 71, 71, 71, 73, 73
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Version 2 of the "next prime" function is "smallest prime > n". This produces A151800.
Maple uses version 2.
According to the "k-tuple" conjecture, a(n) is the initial term of the lexicographically earliest increasing arithmetic progression of n primes; the corresponding common differences are given by A061558. - David W. Wilson, Sep 22 2007
It is easy to show that the initial term of an increasing arithmetic progression of n primes cannot be smaller than a(n). - N. J. A. Sloane (njas(AT)research.att.com), Oct 18 2007
Also, smallest prime bounded by n and 2n inclusively (in accordance with Bertrand's theorem). Smallest prime >n is a(n+1) and is equivalent to smallest prime between n and 2n exclusively. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 01 2007
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REFERENCES
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K. Atanassov, On the 37-th and 38-th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 2, 83-85.
K. Atanassov, On Some of Smarandache's Problems, American Research Press, 1999, 22-26.
J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 202-204.
F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 1993
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
Jens Kruse Andersen, Records for primes in arithmetic progressions
K. Atanassov, On Some of Smarandache's Problems
H. Bottomley, Prime number calculator
Andrew Granville, Prime Number Patterns
Hans Gunter, Puzzle 145. The Inferior Smarandache Prime Part and Superior Smarandache Prime Part functions; Solutions by Jean Marie Charrier, Teresinha DaCosta, Rene Blanch, Richard Kelley and Jim Howell.
K. Matthews, Finding the first prime p=>m
M. L. Perez et al., eds., Smarandache Notions Journal
F. Smarandache, Only Problems, Not Solutions!.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Bertrand's Postulate
Eric Weisstein's World of Mathematics, k-tuple conjecture
Index entries for sequences related to primes in arithmetic progressions
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MAPLE
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A007918 := n-> nextprime(n);
A007918 := n-> nextprime(n-1); - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 09 2008
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PROGRAM
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(PARI) for(x=0, 100, print1(nextprime(x)", ")) - Cino Hilliard (hillcino368(AT)hotmail.com), Jan 15 2007
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CROSSREFS
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Cf. A000040, A007917, A061558, A151800, A151799.
Sequence in context: A135213 A035658 A077018 this_sequence A126111 A122789 A014208
Adjacent sequences: A007915 A007916 A007917 this_sequence A007919 A007920 A007921
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KEYWORD
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nonn,easy,nice
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AUTHOR
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R. Muller and Charles T. Le (charlestle(AT)yahoo.com)
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