OFFSET
1,1
COMMENTS
For a real r>1, a prime p is called an r-gap prime, if there is no prime between r*p and r*q, where q is the next prime after p. In particular, 2-gap primes are in A080192.
In many cases, q=p+2. E.g., among first 1000 terms there are 509 such cases. - Zak Seidov, Jun 29 2015
LINKS
Zak Seidov, Table of n, a(n) for n = 1..10000
MAPLE
filter:= p -> isprime(p) and nextprime(3*p)>3*nextprime(p):
select(filter, [2, seq(2*i+1, i=1..2000)]); # Robert Israel, Jun 29 2015
MATHEMATICA
pQ[p_, r_] := Block[{q = NextPrime@ p}, Union@ PrimeQ@ Range[r*p, r*q] == {False}]; Select[ Prime@ Range@ 380, pQ[#, 3] &] (* Robert G. Wilson v, Sep 18 2011 *)
k = 3; p = 71; Reap[Do[While[NextPrime[k*p] < k*(q = NextPrime[p]), p = q]; Sow[p]; p = q, {1000}]][[2, 1]] (* for first 1000 terms. - Zak Seidov, Jun 29 2015 *)
Prime/@SequencePosition[PrimePi[3*Prime[Range[400]]], {x_, x_}][[;; , 1]] (* Harvey P. Dale, Nov 29 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 14 2011
STATUS
approved