%I
%S 71,107,137,281,347,379,443,461,557,617,641,727,809,827,853,857,991,
%T 1031,1049,1091,1093,1289,1297,1319,1433,1489,1579,1607,1613,1697,
%U 1747,1787,1867,1871,1877,1931,1987,1997,2027,2237,2269,2309,2377,2381,2473,2591
%N 3gap primes: Prime p is a term iff there is no prime between 3*p and 3*q, where q is the next prime after p.
%C For a real r>1, a prime p is called an rgap prime, if there is no prime between r*p and r*q, where q is the next prime after p. In particular, 2gap primes are in A080192.
%C In many cases, q=p+2. E.g., among first 1000 terms there are 509 such cases.  _Zak Seidov_, Jun 29 2015
%H Zak Seidov, <a href="/A195270/b195270.txt">Table of n, a(n) for n = 1..10000</a>
%p filter:= p > isprime(p) and nextprime(3*p)>3*nextprime(p):
%p select(filter, [2,seq(2*i+1,i=1..2000)]); # _Robert Israel_, Jun 29 2015
%t 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 *)
%t 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 *)
%Y Cf. A080192, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Sep 14 2011
