login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038710 a(n) is the smallest prime > product of the first n primes (A002110(n)). 7
2, 3, 7, 31, 211, 2311, 30047, 510529, 9699713, 223092907, 6469693291, 200560490131, 7420738134871, 304250263527281, 13082761331670077, 614889782588491517, 32589158477190044789, 1922760350154212639131, 117288381359406970983379, 7858321551080267055879179 (list; graph; refs; listen; history; text; internal format)
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+prod(k=1, n, prime(k))); \\ Michel Marcus, Sep 25 2016

CROSSREFS

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

Sequence in context: A081947 A046972 A006862 * A241196 A073918 A096350

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)