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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
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
Sequence in context: A339463 A166576 A369250 * A142111 A164289 A243888
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 14 2011
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)