%I #17 Sep 25 2020 05:10:39

%S 1,7,10,49,70,100,343,490,700,1000,2401,3430,4900,7000,10000,16807,

%T 24010,34300,49000,70000,100000,117649,168070,240100,343000,490000,

%U 700000,823543,1000000,1176490,1680700,2401000,3430000,4900000,5764801,7000000

%N Numbers of form 7^i*10^j, with i, j >= 0.

%H Reinhard Zumkeller, <a href="/A025632/b025632.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{n>=1} 1/a(n) = (7*10)/((7-1)*(10-1)) = 35/27. - _Amiram Eldar_, Sep 25 2020

%F a(n) ~ exp(sqrt(2*log(7)*log(10)*n)) / sqrt(70). - _Vaclav Kotesovec_, Sep 25 2020

%t n = 10^6; Flatten[Table[7^i*10^j, {i, 0, Log[7, n]}, {j, 0, Log10[n/7^i]}]] // Sort (* _Amiram Eldar_, Sep 25 2020 *)

%o (Haskell)

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

%o a025632 n = a025632_list !! (n-1)

%o a025632_list = f $ singleton (1,0,0) where

%o f s = y : f (insert (7 * 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*=7)); Set(v) \\ _Charles R Greathouse IV_, Jan 10 2018

%Y Cf. A025612, A025616, A025621, A025625, A025629, A025634, A025635, A108761, A003596, A003597, A107988, A003598, A108698, A003599, A107788, A108687, A108779, A108090.

%K easy,nonn

%O 1,2

%A _David W. Wilson_