A061785 - OEIS

%I #20 Apr 21 2024 14:01:44

%S 2,4,6,9,11,13,16,18,20,23,25,27,30,32,34,37,39,41,44,46,48,51,53,55,

%T 58,60,62,65,67,69,71,74,76,78,81,83,85,88,90,92,95,97,99,102,104,106,

%U 109,111,113,116,118,120,123,125,127,130,132,134,136,139,141,143,146,148

%N a(n) = m such that 2^m < 5^n < 2^(m+1).

%C The Beatty sequence for log_2(5) (A020858). The asymptotic density of this sequence is log_5(2) (A152675). - _Amiram Eldar_, Apr 09 2021

%C One less than the length of 5^n written in binary. Could and should be extended to a(0) = 0 (with definition corrected to "2^m <= ..."). - _M. F. Hasler_, Apr 17 2024

%H Amiram Eldar, <a href="/A061785/b061785.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(n*log_2(5)). - _M. F. Hasler_, Apr 17 2024

%e a(2) = 4 since 2^4 < 5^2 < 2^(4+1).

%t Table[Floor[n*Log2[5]], {n, 100}] (* _Amiram Eldar_, Apr 09 2021 *)

%o (PARI) a(n) = floor(n*log(5)/log(2)) \\ _Michel Marcus_, Jul 27 2013

%Y Cf. A020858, A152675.

%Y Cf. A118738 (Hamming weight of 5^n).

%K nonn,easy

%O 1,1

%A _Lekraj Beedassy_, May 09 2003

%E Corrected and extended by _John W. Layman_, May 09 2003