

A195325


Least ngap prime: a(n) = least prime p for which there is no prime between n*p and n*q, where q is the next prime after p.


14



2, 59, 71, 29, 59, 149, 191, 641, 149, 347, 809, 461, 3371, 1487, 857, 1301, 1877, 5849, 4721, 9239, 4271, 1619, 1481, 20507, 20981, 32117, 13337, 19379, 24977, 48779, 20441, 25301, 5651, 37991, 17747, 43577, 176777, 145757, 191249, 84809, 150209, 11717
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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:


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



STATUS

approved



