OFFSET
1,4
COMMENTS
Compare to 2^i * 3^j, the 3-smooth numbers, cf. A003586.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = floor(z*A003586(k)), k>0 and z in {1,sqrt(2),sqrt(3),sqrt(6)}.
EXAMPLE
. n | a(n) || i | j | u^i * v^j with u = sqrt(2), v = sqrt(3)
. ----+------++---+---+----------------------------------------
. 1 | 1 || 0 | 0 | u^0 * v^0 = 1.0
. 2 | 1 || 1 | 0 | u^1 * v^0 = 1 * u = 1.414213...
. 3 | 1 || 0 | 1 | u^0 * v^1 = 1 * v = 1.732050...
. 4 | 2 || 2 | 0 | u^2 * v^0 = 2 = 2.0
. 5 | 2 || 1 | 1 | u^1 * v^1 = 1 * sqrt(6) = 2.449489...
. 6 | 2 || 3 | 0 | u^3 * v^0 = 2 * u = 2.828427...
. 7 | 3 || 0 | 2 | u^0 * v^2 = 3 = 3.0
. 8 | 3 || 2 | 1 | u^2 * v^1 = 2 * v = 3.464101...
. 9 | 4 || 4 | 0 | u^4 * v^0 = 2^2 = 4.0
. 10 | 4 || 1 | 2 | u^1 * v^2 = 3 * u = 4.242640...
. 11 | 4 || 3 | 1 | u^3 * v^1 = 2 * sqrt(6) = 4.898979...
. 12 | 5 || 0 | 3 | u^0 * v^3 = 3 * v = 5.196152...
. 13 | 5 || 5 | 0 | u^5 * v^0 = 2^2 * u = 5.656854...
. 14 | 6 || 2 | 2 | u^2 * v^2 = 2 * 3 = 6.0
. 15 | 6 || 4 | 1 | u^4 * v^1 = 2^2 * v = 6.928203...
. 16 | 7 || 1 | 3 | u^1 * v^3 = 3 * sqrt(6) = 7.348469...
. 17 | 8 || 6 | 0 | u^6 * v^0 = 2^3 = 8.0
. 18 | 8 || 3 | 2 | u^3 * v^2 = 2 * 3 * u = 8.485281...
. 19 | 9 || 0 | 4 | u^0 * v^4 = 3^2 = 9.0
. 20 | 9 || 5 | 1 | u^5 * v^1 = 2^2 * sqrt(6) = 9.797958... .
PROG
(Haskell)
import Data.Set (Set, singleton, insert, deleteFindMin)
a247366 n = a247366_list !! (n-1)
a247366_list = h $ singleton (1, 0, 0) where
h :: Set (Double, Int, Int) -> [Integer]
h s = (floor x) : h (insert (f i (j + 1)) $ insert (f (i + 1) j) s')
where ((x, i, j), s') = deleteFindMin s
f :: Int -> Int -> (Double, Int, Int)
f u v = (2 ^^ uh * 3 ^^ vh * g ur vr, u, v) where
g 0 0 = 1; g 0 1 = sqrt 3; g 1 0 = sqrt 2; g 1 1 = sqrt 6
(uh, ur) = divMod u 2; (vh, vr) = divMod v 2
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 14 2014
STATUS
approved