|
|
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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|