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A195270 3-gap 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 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

Cf. A080192, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.

Sequence in context: A339466 A339463 A166576 * A142111 A164289 A243888

Adjacent sequences:  A195267 A195268 A195269 * A195271 A195272 A195273

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Sep 14 2011

STATUS

approved

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Last modified August 17 05:07 EDT 2022. Contains 356184 sequences. (Running on oeis4.)