OFFSET
0,1
COMMENTS
The lower "envelope" of the sequence is prime(n+1)^2. See also Fortune-conjecture (A005235).
For some n, c=prime(n+1)^2; for others, it is larger, even not necessarily divisible by prime(n+1). E.g., at n=11, prime(11)=31 and a(11) = 1591 = 37*43 = prime(12)*prime(14), while for n=59, a(59) = 97969 = 313^2 = prime(65)^2, etc. Adding these to the suitable primorial numbers, primes are obtained.
Conjecture: lim inf_{n->oo} a(n)/prime(n+1)^2 = 1 < lim sup_{n->oo} a(n)/prime(n+1)^2 = 2. - Charles R Greathouse IV and Thomas Ordowski, Apr 24 2015
Conjecture: all the terms in this sequence have exactly two prime factors. This conjecture is true for the first 133 terms. - Dmitry Kamenetsky, Jan 06 2019
LINKS
Dmitry Kamenetsky, Table of n, a(n) for n = 0..133
PROG
(PARI) a(n) = {my(q = prod(i=1, n, prime(i))); forcomposite(c = 1, , if (isprime(q+c), return(c); ); ); } \\ Michel Marcus, May 24 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 04 2000
EXTENSIONS
Name edited by Tom Edgar, Jun 08 2015
a(0) prepended by Dmitry Kamenetsky, Jan 06 2019
STATUS
approved