cp's OEIS Frontend

A025635 Numbers of form 9^i*10^j, with i, j >= 0.

%I A025635 #25 Jul 06 2025 10:20:57
%S A025635 1,9,10,81,90,100,729,810,900,1000,6561,7290,8100,9000,10000,59049,
%T A025635 65610,72900,81000,90000,100000,531441,590490,656100,729000,810000,
%U A025635 900000,1000000,4782969,5314410,5904900,6561000,7290000,8100000,9000000
%N A025635 Numbers of form 9^i*10^j, with i, j >= 0.
%H A025635 Reinhard Zumkeller, <a href="/A025635/b025635.txt">Table of n, a(n) for n = 1..10000</a>
%F A025635 Sum_{n>=1} 1/a(n) = 5/4. - _Amiram Eldar_, Mar 29 2025
%F A025635 a(n) = 9^A025683(n) * 10^A025691(n). - _R. J. Mathar_, Jul 06 2025
%t A025635 With[{max = 10^7}, Flatten[Table[9^i*10^j, {i, 0, Log[9, max]}, {j, 0, Log[10, max/9^i]}]] // Sort] (* _Amiram Eldar_, Mar 29 2025 *)
%o A025635 (Haskell)
%o A025635 import Data.Set (singleton, deleteFindMin, insert)
%o A025635 a025635 n = a025635_list !! (n-1)
%o A025635 a025635_list = f $ singleton (1,0,0) where
%o A025635    f s = y : f (insert (9 * y, i + 1, j) $ insert (10 * y, i, j + 1) s')
%o A025635          where ((y, i, j), s') = deleteFindMin s
%o A025635 -- _Reinhard Zumkeller_, May 15 2015
%o A025635 (PARI) list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 10), N=10^n; while(N<=lim, listput(v, N); N*=9)); Set(v) \\ _Charles R Greathouse IV_, Jan 10 2018
%o A025635 (Python)
%o A025635 from sympy import integer_log
%o A025635 def A025635(n):
%o A025635     def bisection(f,kmin=0,kmax=1):
%o A025635         while f(kmax) > kmax: kmax <<= 1
%o A025635         kmin = kmax >> 1
%o A025635         while kmax-kmin > 1:
%o A025635             kmid = kmax+kmin>>1
%o A025635             if f(kmid) <= kmid:
%o A025635                 kmax = kmid
%o A025635             else:
%o A025635                 kmin = kmid
%o A025635         return kmax
%o A025635     def f(x): return n+x-sum(integer_log(x//10**i,9)[0]+1 for i in range(integer_log(x,10)[0]+1))
%o A025635     return bisection(f,n,n) # _Chai Wah Wu_, Mar 25 2025
%Y A025635 Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A108761, A003596, A003597, A107988, A003598, A108698, A003599, A107788, A108687, A108779, A108090.
%K A025635 easy,nonn
%O A025635 1,2
%A A025635 _David W. Wilson_