

A195270


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.


11



71, 107, 137, 281, 347, 379, 443, 461, 557, 617, 641, 727, 809, 827, 853, 857, 991, 1031, 1049, 1091, 1093, 1289, 1297, 1319, 1433, 1489, 1579, 1607, 1613, 1697, 1747, 1787, 1867, 1871, 1877, 1931, 1987, 1997, 2027, 2237, 2269, 2309, 2377, 2381, 2473, 2591
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OFFSET

1,1


COMMENTS

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.
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 *)


CROSSREFS

Cf. A080192, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.
Sequence in context: A234962 A166252 A166576 * A142111 A164289 A243888
Adjacent sequences: A195267 A195268 A195269 * A195271 A195272 A195273


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Sep 14 2011


STATUS

approved



