OFFSET
1,2
COMMENTS
Subsequence of 3-smooth numbers, cf. A003586.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
F. Javier de Vega, An extension of Furstenberg's theorem of the infinitude of primes, arXiv:2003.13378 [math.NT], 2020.
FORMULA
Sum_{n>=1} 1/a(n) = (3*4)/((3-1)*(4-1)) = 2. - Amiram Eldar, Sep 24 2020
a(n) ~ exp(sqrt(2*log(3)*log(4)*n)) / sqrt(12). - Vaclav Kotesovec, Sep 24 2020
MATHEMATICA
n = 10^5; Flatten[Table[3^i*4^j, {i, 0, Log[3, n]}, {j, 0, Log[4, n/3^i]}]] // Sort (* Amiram Eldar, Sep 24 2020 *)
PROG
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a025613 n = a025613_list !! (n-1)
a025613_list = f $ singleton 1
where f s = m : (f $ insert (3*m) $ insert (4*m) s')
where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011
(PARI) list(lim)=my(v=List(), N); for(n=0, logint(lim\1, 3), N=3^n; while(N<=lim, listput(v, N); N<<=2)); Set(v) \\ Charles R Greathouse IV, Sep 10 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved