%I #17 Sep 25 2020 06:02:59

%S 1,3,9,10,27,30,81,90,100,243,270,300,729,810,900,1000,2187,2430,2700,

%T 3000,6561,7290,8100,9000,10000,19683,21870,24300,27000,30000,59049,

%U 65610,72900,81000,90000,100000,177147,196830,218700,243000,270000

%N Numbers of form 3^i*10^j, with i, j >= 0.

%H Reinhard Zumkeller, <a href="/A025616/b025616.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{n>=1} 1/a(n) = (3*10)/((3-1)*(10-1)) = 5/3. - _Amiram Eldar_, Sep 25 2020

%F a(n) ~ exp(sqrt(2*log(3)*log(10)*n)) / sqrt(30). - _Vaclav Kotesovec_, Sep 25 2020

%t n = 10^6; Flatten[Table[3^i*10^j, {i, 0, Log[3, n]}, {j, 0, Log10[n/3^i]}]] // Sort (* _Amiram Eldar_, Sep 25 2020 *)

%o (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a025616 n = a025616_list !! (n-1)

%o a025616_list = f $ singleton (1,0,0) where

%o f s = y : f (insert (3 * y, i + 1, j) $ insert (10 * y, i, j + 1) s')

%o where ((y, i, j), s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, May 15 2015

%o (PARI) list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 10), N=10^n; while(N<=lim, listput(v, N); N*=3)); Set(v) \\ _Charles R Greathouse IV_, Jan 10 2018

%Y Cf. A025612, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003596, A003597, A107988, A003598, A108698, A003599, A107788, A108687, A108779, A108090.

%K easy,nonn

%O 1,2

%A _David W. Wilson_