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%I #69 Mar 12 2023 17:29:57
%S 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 29,29,29,29,31,31,37,37,37,37,37,37,41,41,41,41,43,43,47,47,47,47,53,
%U 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
%N Least prime > n (version 2 of the "next prime" function).
%C Version 1 of the "next prime" function is A007918: smallest prime >= n.
%C Maple's nextprime() is this version 2; PARI/GP's nextprime() is version 1.
%C See A007918 for references and further information.
%C 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
%C Conjecture: if n > 3, then a(n) < n^(n^(1/n)). - _Thomas Ordowski_, Feb 23 2023
%H Daniel Forgues, <a href="/A151800/b151800.txt">Table of n, a(n) for n = 0..100000</a>
%F a(n) = A007918(n+1).
%F a(n) = 1 + Sum_{k=1..2n} (floor((n!^k)/k!) - floor(((n!^k)-1)/k!)). - _Anthony Browne_, May 11 2016
%p map(nextprime,[$0..100]); # _Robert Israel_, Jul 15 2015
%t NextPrime[Range[0,80]] (* _Harvey P. Dale_, May 21 2011 *)
%o (Maxima) makelist(next_prime(n), n, 0, 73); \\ _Bruno Berselli_, May 20 2011
%o (Haskell) a151800 = a007918 . (+ 1) -- _Reinhard Zumkeller_, Jul 26 2012
%o (PARI) a(n)=nextprime(n+1) \\ _Charles R Greathouse IV_, Apr 28 2015
%o (Magma) [NextPrime(n): n in [0..80]]; // _Vincenzo Librandi_, Jan 14 2016
%o (Python)
%o from sympy import nextprime
%o def A151800(n):
%o return nextprime(n) # _Chai Wah Wu_, Feb 28 2018
%Y Cf. A000040, A007917, A007918, A061558, A151799, A317357.
%K nonn,easy,nice
%O 0,1
%A _N. J. A. Sloane_, Jun 29 2009
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