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 A007918 Least prime >= n (version 1 of the "next prime" function). 99
 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; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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, 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, Jan 01 2007 REFERENCES K. Atanassov, On the 37th and 38th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 2, 83-85. LINKS 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 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. 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. J. Sondow and Eric Weisstein, Bertrand's Postulate, World of Mathematics Eric Weisstein's World of Mathematics, Next Prime, k-tuple conjecture FORMULA For n > 1: a(n) = A000040(A049084(A007917(n)) + 1 - A010051(n)). - Reinhard Zumkeller, Jul 26 2012 a(n) = A151800(n-1). - Seiichi Manyama, Apr 02 2018 MAPLE A007918 := n-> nextprime(n-1); # M. F. Hasler, Apr 09 2008 MATHEMATICA NextPrime[Range[-1, 72]] (* Jean-François Alcover, Apr 18 2011 *) PROG (PARI 2.4.3 and later) A007918=nextprime  \\ M. F. Hasler, Jun 24 2011 (PARI 2.4.2 and earlier) A007918(n)=nextprime(n)  \\ M. F. Hasler, Jun 24 2011 (PARI) for(x=0, 100, print1(nextprime(x)", ")) \\ Cino Hilliard, Jan 15 2007 (Haskell) a007918 n = a007918_list !! n a007918_list = 2 : 2 : 2 : concat (zipWith               (\p q -> (replicate (fromInteger(q - p)) q))                                    a000040_list \$ tail a000040_list) -- Reinhard Zumkeller, Jul 26 2012 (MAGMA) [2] cat [NextPrime(n-1): n in [1..80]]; // Vincenzo Librandi, Jan 14 2016 CROSSREFS Cf. A000040, A007917, A008407, A020497, A061558, A151799, A151800, A171400. Sequence in context: A304683 A035658 A077018 * A278167 A239470 A320786 Adjacent sequences:  A007915 A007916 A007917 * A007919 A007920 A007921 KEYWORD nonn,easy,nice AUTHOR R. Muller and Charles T. Le (charlestle(AT)yahoo.com) STATUS approved

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Last modified October 16 08:15 EDT 2019. Contains 328051 sequences. (Running on oeis4.)