Search: id:A007918
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%I A007918
%S A007918 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,
%T A007918 29,29,29,29,31,31,37,37,37,37,37,37,41,41,41,41,43,43,47,47,47,47,53,
               53,
%U A007918 53,53,53,53,59,59,59,59,59,59,61,61,67,67,67,67,67,67,71,71,71,71,73,
               73
%N A007918 Least prime >= n (version 1 of the "next prime" function).
%C A007918 Version 2 of the "next prime" function is "smallest prime > n". This 
               produces A151800.
%C A007918 Maple uses version 2.
%C A007918 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
%C A007918 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
%C A007918 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
%D A007918 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.
%D A007918 K. Atanassov, On Some of Smarandache's Problems, American Research Press, 
               1999, 22-26.
%D A007918 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.
%D A007918 F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 
               1993
%H A007918 T. D. Noe, <a href="b007918.txt">Table of n, a(n) for n=0..10000</a>
%H A007918 Jens Kruse Andersen, <a href="http://users.cybercity.dk/~dsl522332/math/
               aprecords.htm">Records for primes in arithmetic progressions</a>
%H A007918 K. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">
               On Some of Smarandache's Problems</a>
%H A007918 H. Bottomley, <a href="http://www.btinternet.com/~se16/js/prime.htm">
               Prime number calculator</a>
%H A007918 Andrew Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimePattMonthly.pdf">
               Prime Number Patterns</a>
%H A007918 Hans Gunter, <a href="http://primepuzzles.net/puzzles/puzz_145.htm">Puzzle 
               145. The Inferior Smarandache Prime Part and Superior Smarandache 
               Prime Part functions</a>; Solutions by Jean Marie Charrier, Teresinha 
               DaCosta, Rene Blanch, Richard Kelley and Jim Howell.
%H A007918 K. Matthews, <a href="http://www.numbertheory.org/php/nprime.html">Finding 
               the first prime p=>m</a>
%H A007918 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A007918 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>.
%H A007918 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NextPrime.html">Link to a section of The World of Mathematics.</a>
%H A007918 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BertrandsPostulate.html">Bertrand's Postulate</a>
%H A007918 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               k-TupleConjecture.html">k-tuple conjecture</a>
%H A007918 <a href="Sindx_Pri.html#primes_AP">Index entries for sequences related 
               to primes in arithmetic progressions</a>
%p A007918 A007918 := n-> nextprime(n);
%p A007918 A007918 := n-> nextprime(n-1); - M. F. Hasler (www.univ-ag.fr/~mhasler), 
               Apr 09 2008
%o A007918 (PARI) for(x=0,100,print1(nextprime(x)",")) - Cino Hilliard (hillcino368(AT)hotmail.com), 
               Jan 15 2007
%Y A007918 Cf. A000040, A007917, A061558, A151800, A151799.
%Y A007918 Sequence in context: A135213 A035658 A077018 this_sequence A126111 A122789 
               A014208
%Y A007918 Adjacent sequences: A007915 A007916 A007917 this_sequence A007919 A007920 
               A007921
%K A007918 nonn,easy,nice
%O A007918 0,1
%A A007918 R. Muller and Charles T. Le (charlestle(AT)yahoo.com)

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