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A151800 Least prime > n (version 2 of the "next prime" function). 155
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, 79 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Version 1 of the "next prime" function is A007918: smallest prime >= n.

Maple's nextprime() is this version 2; PARI/GP's nextprime() is version 1.

See A007918 for references and further information.

a(n) is the smallest number greater than one that is not divisible by any 1 < k <= n. Consider a multi-round election in which, in each round, voters each cast one vote for one of the remaining candidates. Then, any candidates which receive the fewest votes in that round are eliminated. This repeats until either one candidate remains, who wins the election, or no candidates remain. a(n) is the smallest nontrivial number of voters that can guarantee a winner if the election initially has n > 0 candidates. This is a consequence of the first fact. - Thomas Anton, Mar 30 2020

LINKS

Daniel Forgues, Table of n, a(n) for n = 0..100000

FORMULA

a(n) = A007918(n+1).

a(n) = 1 + Sum_{k=1..2n}(floor((n!^k)/k!)-floor(((n!^k)-1)/k!)). - Anthony Browne, May 11 2016

MAPLE

map(nextprime, [$0..100]); # Robert Israel, Jul 15 2015

MATHEMATICA

NextPrime[Range[0, 80]] (* Harvey P. Dale, May 21 2011 *)

PROG

(Maxima) makelist(next_prime(n), n, 0, 73); \\ Bruno Berselli, May 20 2011

(Haskell) a151800 = a007918 . (+ 1)  -- Reinhard Zumkeller, Jul 26 2012

(PARI) a(n)=nextprime(n+1) \\ Charles R Greathouse IV, Apr 28 2015

(MAGMA) [NextPrime(n): n in [0..80]]; // Vincenzo Librandi, Jan 14 2016

(Python)

from sympy import nextprime

def A151800(n):

    return nextprime(n) # Chai Wah Wu, Feb 28 2018

CROSSREFS

Cf. A000040, A007917, A007918, A061558, A151799, A317357.

Sequence in context: A090473 A113636 A262463 * A259430 A290838 A056896

Adjacent sequences:  A151797 A151798 A151799 * A151801 A151802 A151803

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Jun 29 2009

STATUS

approved

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Last modified January 24 09:05 EST 2021. Contains 340398 sequences. (Running on oeis4.)