A025632 Numbers of form 7^i*10^j, with i, j >= 0.

1, 7, 10, 49, 70, 100, 343, 490, 700, 1000, 2401, 3430, 4900, 7000, 10000, 16807, 24010, 34300, 49000, 70000, 100000, 117649, 168070, 240100, 343000, 490000, 700000, 823543, 1000000, 1176490, 1680700, 2401000, 3430000, 4900000, 5764801, 7000000

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Links

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

Crossrefs

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

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a025632 n = a025632_list !! (n-1)
a025632_list = f $ singleton (1,0,0) where
   f s = y : f (insert (7 * y, i + 1, j) $ insert (10 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015

Mathematica

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 *)

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

Formula

Sum_{n>=1} 1/a(n) = (7*10)/((7-1)*(10-1)) = 35/27. - Amiram Eldar, Sep 25 2020

a(n) ~ exp(sqrt(2*log(7)*log(10)*n)) / sqrt(70). - Vaclav Kotesovec, Sep 25 2020

a(n) = 7^A025671(n) * 10^A025689(n). - R. J. Mathar, Jul 06 2025