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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
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
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 *)
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 14 2011
STATUS
approved