A037151 - OEIS

%I #25 May 22 2022 14:30:38

%S 2,3,7,29,127,727,5051,40343,362897,3628811,39916801,479001629,

%T 6227020867,87178291219,1307674368043,20922789888023,355687428096031,

%U 6402373705728037,121645100408832089,2432902008176640029,51090942171709440031,1124000727777607680031

%N Smallest prime > n!.

%H Hugo Pfoertner, <a href="/A037151/b037151.txt">Table of n, a(n) for n = 1..450</a>

%H Antonín Čejchan, Michal Křížek, and Lawrence Somer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Krizek/krizek3.html">On Remarkable Properties of Primes Near Factorials and Primorials</a>, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4.

%F a(n) = A151800(A000142(n)) = A000142(n) + A033932(n).

%t PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k]; Table[PrimeNext[n! ],{n,40}] (* _Vladimir Joseph Stephan Orlovsky_, May 30 2010 *)

%t Table[NextPrime[n!],{n,25}] (* _Harvey P. Dale_, Dec 12 2010 *)

%o (Python)

%o from sympy import factorial, nextprime

%o def a(n): return nextprime(factorial(n))

%o print([a(n) for n in range(1, 23)]) # _Michael S. Branicky_, May 22 2022

%Y Cf. A000142, A033932, A087421, A151800.

%K nonn

%O 1,1

%A _Jud McCranie_

%E Extended by _Ray Chandler_, Mar 07 2010