0,1

Version 2 of the "next prime" function is "smallest prime > n". This produces almost the same sequence of numbers, except one of the initial 2's is omitted.

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). - njas, 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

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

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

A007918 := n-> nextprime(n);

A007918 := n-> nextprime(n-1); - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 09 2008

(PARI) for(x=0, 100, print1(nextprime(x)", ")) - Cino Hilliard (hillcino368(AT)hotmail.com), Jan 15 2007

Cf. A000040, A007917, A061558.

Sequence in context: A135213 A035658 A077018 this_sequence A126111 A122789 A014208

Adjacent sequences: A007915 A007916 A007917 this_sequence A007919 A007920 A007921

nonn,easy,nice

R. Muller and Charles T. Le (charlestle(AT)yahoo.com)