A025633 Numbers of form 8^i*9^j, with i, j >= 0.

1, 8, 9, 64, 72, 81, 512, 576, 648, 729, 4096, 4608, 5184, 5832, 6561, 32768, 36864, 41472, 46656, 52488, 59049, 262144, 294912, 331776, 373248, 419904, 472392, 531441, 2097152, 2359296, 2654208, 2985984, 3359232, 3779136, 4251528, 4782969

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A025611 and A025615.

Programs

Mathematica

n = 10^6; Flatten[Table[8^i*9^j, {i, 0, Log[8, n]}, {j, 0, Log[9, n/8^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

PARI

list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 9), N=9^n; while(N<=lim, listput(v, N); N<<=3)); Set(v) \\ Charles R Greathouse IV, Jan 10 2018

Formula

Sum_{n>=1} 1/a(n) = (8*9)/((8-1)*(9-1)) = 9/7. - Amiram Eldar, Sep 25 2020

a(n) ~ exp(sqrt(2*log(8)*log(9)*n)) / sqrt(72). - Vaclav Kotesovec, Sep 25 2020

a(n) = 8^A025676(n) * 9^A025682(n). - R. J. Mathar, Jul 06 2025