A037151 Smallest prime > n!.

2, 3, 7, 29, 127, 727, 5051, 40343, 362897, 3628811, 39916801, 479001629, 6227020867, 87178291219, 1307674368043, 20922789888023, 355687428096031, 6402373705728037, 121645100408832089, 2432902008176640029, 51090942171709440031, 1124000727777607680031

Offset

1,1

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..450

Antonín Čejchan, Michal Křížek, and Lawrence Somer, On Remarkable Properties of Primes Near Factorials and Primorials, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4.

Formula

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

Mathematica

PrimeNext[n_]:=Module[{k}, k=n+1; While[ !PrimeQ[k], k++ ]; k]; Table[PrimeNext[n! ], {n, 40}] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
Table[NextPrime[n!], {n, 25}] (* Harvey P. Dale, Dec 12 2010 *)

Prog

(Python)
from sympy import factorial, nextprime
def a(n): return nextprime(factorial(n))
print([a(n) for n in range(1, 23)]) # Michael S. Branicky, May 22 2022

Crossrefs

Cf. A000142, A033932, A087421, A151800.

Sequence in context: A084435 A072469 A004062 * A326358 A008840 A268477

Adjacent sequences: A037148 A037149 A037150 * A037152 A037153 A037154

Keyword

nonn

Author

Jud McCranie

Extensions

Extended by Ray Chandler, Mar 07 2010

Status

approved