OFFSET
1,1
COMMENTS
Such a prime always exists.
The sequence is unbounded.
Conjecture. For n >= 2, a(n) is a lesser of twin primes (A001359). This implies the twin prime conjecture. - Vladimir Shevelev, Sep 15 2011
If a member of this sequence is not the lesser of a twin prime pair, it is greater than 10^10. - Charles R Greathouse IV, Sep 15 2011
A dual sequence: b(n)= least prime p for which there is no prime between n*q and n*p, where q is the previous prime before p. Evidently, b(n) is the next prime after a(n): 3,61,73,31,..., and for n>=2, by the same conjecture, b(n) is a greater of twin primes.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..169, (first 100 terms from Alois P. Heinz)
MAPLE
a:= proc(n) local p, q;
p:= 2; q:= nextprime(p);
while nextprime(n*p) < (n*q) do
p, q:= q, nextprime(q)
od; p
end:
seq (a(n), n=1..25); # Alois P. Heinz, Sep 15 2011
MATHEMATICA
pQ[p_, r_] := Block[{q = NextPrime[p]}, NextPrime[r*p]> r*q]; f[n_] := Block[{p = 2}, While[ !pQ[p, n], p = NextPrime[p]]; p]; f[1] = 2; Array[f, 42] (* Robert G. Wilson v, Sep 18 2011 *) (* Revised by Zak Seidov, Sep 19 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 15 2011
STATUS
approved