A038710 a(n) is the smallest prime > product of the first n primes (A002110(n)).

2, 3, 7, 31, 211, 2311, 30047, 510529, 9699713, 223092907, 6469693291, 200560490131, 7420738134871, 304250263527281, 13082761331670077, 614889782588491517, 32589158477190044789, 1922760350154212639131, 117288381359406970983379, 7858321551080267055879179

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Formula

a(n) = A002110(n) + A038711(n). - Alois P. Heinz, Mar 16 2020

Example

for n=1,2,3,4,5,11,75, A002110(n)+1 gives smaller primes than A002110(n)+p, where p is a fortunate number (prime). At n=5, both 2311 and 2333 are primes but the first is smaller.

Maple

p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
a:= n-> nextprime(p(n)):
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 16 2020

Mathematica

nmax = 2^16384; npd = 1; n = 1; npd = npd*Prime[n]; While[npd < nmax, cp = npd + 1; While[ ! (PrimeQ[cp]), cp = cp + 2]; Print[cp]; n = n + 1; npd = npd*Prime[n]] (* Lei Zhou, Feb 15 2005 *)
NextPrime/@FoldList[Times, 1, Prime[Range[25]]] (* Harvey P. Dale, Dec 17 2010 *)

Prog

(PARI) a(n) = nextprime(1+factorback(primes(n))); \\ Michel Marcus, Sep 25 2016; Dec 24 2022
(Python)
from sympy import nextprime, primorial
def a(n): return nextprime(primorial(n) if n else 1)
print([a(n) for n in range(20)]) # Michael S. Branicky, Dec 24 2022

Crossrefs

Cf. A002110, A005235, A007014, A018239, A035345, A038711.

Sequence in context: A081947 A046972 A006862 * A241196 A073918 A018239

Adjacent sequences: A038707 A038708 A038709 * A038711 A038712 A038713

Keyword

nonn

Author

Labos Elemer, May 02 2000

Extensions

Offset corrected, incorrect comment and formula removed, and more terms added by Jinyuan Wang, Mar 16 2020

Status

approved