A108761 Numbers of the form (10^i)*(13^j), with i, j >= 0.

1, 10, 13, 100, 130, 169, 1000, 1300, 1690, 2197, 10000, 13000, 16900, 21970, 28561, 100000, 130000, 169000, 219700, 285610, 371293, 1000000, 1300000, 1690000, 2197000, 2856100, 3712930, 4826809, 10000000, 13000000, 16900000

Offset: 1

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jun 24 2005

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A107326, A107364, A107462, A107466, A107710, A108056, A107764, A108748, A108090.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a108761 n = a108761_list !! (n-1)
a108761_list = f $ singleton (1,0,0) where
   f s = y : f (insert (10 * y, i + 1, j) $ insert (13 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015

Mathematica

n = 10^7; Flatten[Table[10^i*13^j, {i, 0, Log10[n]}, {j, 0, Log[13, n/10^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Formula

Sum_{n>=1} 1/a(n) = (10*13)/((10-1)*(13-1)) = 65/54. - Amiram Eldar, Sep 25 2020

a(n) ~ exp(sqrt(2*log(10)*log(13)*n)) / sqrt(130). - Vaclav Kotesovec, Sep 25 2020