OFFSET
1,1
COMMENTS
Conjecture: All terms are prime.
While Fortune's conjecture (A005235) uses products of primes, this sequence uses products of composite numbers (more exactly: of nonprimes, because 1 belongs to them). It looks like all multiples of prime(n)# (except some powers) lead to a sequence which contains only prime numbers.
EXAMPLE
n = 1; prime(1)!/prime(1)# = 2/2 = 1; p = nextprime(1+1) = 3; a(1) = 3-1 = 2.
PROG
(MuPAD) q:=1; p:=1; for i from 1 to 100 do q:=nextprime(q+1); p:=p*q; N:=nextprime((fact(q)/p)+2)-fact(q)/p; print(i, N); end_for:
(PARI) A092435(n)=prime(n)!/prod(i=1, n, prime(i))
a(n)=my(t=A092435(n)); nextprime(t+2)-t \\ Charles R Greathouse IV, Oct 23 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Werner D. Sand, Oct 23 2014
STATUS
approved