%I #26 Mar 07 2024 05:40:03
%S 0,1,2,3,1,2,3,2,4,2,1,2,11,2,1,11,1,1,134,2,2,2,1,4,1,1,3,1,7,1,13,1,
%T 3,5,1,1,1,8,1,3,4,1,1,1,3,4,1,3,1,4,1,4,1,3,40,1,1,5,4,3,3,1,3,1,2,6,
%U 1,1,2,28,11,1,71,2,1,4,8,5,1,2,1,1,14
%N Continued fraction expansion of log_2((sqrt(5)+1)/2) = 0.6942419... = A242208.
%C This number is also the solution to 1 + 2^x = 4^x, or 1 + 1/2^x = 2^x, which clarifies the relation to Phi = (sqrt(5)+1)/2, solution to 1 + 1/x = x.
%H Paolo Xausa, <a href="/A328912/b328912.txt">Table of n, a(n) for n = 0..10000</a>
%e log_2((sqrt(5)+1)/2) = 0.6942419... = 0 + 1/(1 + 1/(2 + 1/(3 + 1/(1 + ...))))
%t ContinuedFraction[Log2[GoldenRatio], 100] (* _Paolo Xausa_, Mar 07 2024 *)
%o (PARI) localprec(1000); contfrac(log(sqrt(5)+1)/log(2)-1)
%Y Cf. A242208, A001622 (decimals of Phi), A000012 (cont. frac. of Phi).
%K nonn,cofr
%O 0,3
%A _M. F. Hasler_, Oct 31 2019
%E Some terms corrected by _Paolo Xausa_, Mar 07 2024