A035345 Smallest prime > prime(1)*prime(2)*...*prime(n)+1.

3, 5, 11, 37, 223, 2333, 30047, 510529, 9699713, 223092907, 6469693291, 200560490197, 7420738134871, 304250263527281, 13082761331670077, 614889782588491517, 32589158477190044789, 1922760350154212639131

Offset

0,1

Links

Table of n, a(n) for n=0..17.

S. W. Golomb, The evidence for Fortune's conjecture, Math. Mag. 54 (1981), 209-210.

Eric Weisstein's World of Mathematics, Fortunate Prime

Formula

a(n) = A002110(n) + A005235(n) for n > 0. - Jonathan Sondow, Dec 02 2015

Example

Next prime after 2*3*5 + 1 = 31 is 37, so a(3)=37.

Mathematica

Table[NextPrime[Product[Prime@ k, {k, n}] + 1], {n, 0, 17}] (* Michael De Vlieger, Dec 02 2015 *)

Prog

(PARI) a(n) = nextprime(2+factorback(primes(n))); \\ Michel Marcus, Dec 24 2022
(Python)
from sympy import nextprime, primorial
def a(n): return nextprime(1 + (primorial(n) if n else 1))
print([a(n) for n in range(18)]) # Michael S. Branicky, Dec 24 2022

Crossrefs

Cf. A002110, A005235, A006862, A038710.

Sequence in context: A307140 A254402 A060881 * A254401 A174915 A162250

Adjacent sequences: A035342 A035343 A035344 * A035346 A035347 A035348

Keyword

nonn

Author

N. J. A. Sloane

Status

approved