%I #22 Nov 26 2025 15:59:39

%S 1,4,4,0,4,2,0,0,9,0,4,1,2,5,5,6,4,7,9,0,1,7,5,5,1,4,9,9,5,8,7,8,6,3,

%T 8,0,2,4,5,8,6,0,4,1,4,2,6,8,4,0,5,6,0,8,1,6,4,5,4,4,1,7,2,9,5,6,6,5,

%U 1,3,2,8,4,3,5,2,9,9,0,3,6,7,2,7,9,5,2,8,2,2,0,4,9,7,3,5,7,5,9,1,6,3,1,2,7

%N Decimal expansion of log base phi of 2.

%C The fractal dimension of the goldpoint snowflake (Turner, 2003). - _Amiram Eldar_, Jan 11 2022

%D Krassimir Atanassova, Vassia Atanassova, Anthony Shannon and John Turner, New Visual Perspectives on Fibonacci Numbers, World Scientific, 2002, p. 218.

%H Greg Kuperberg, <a href="https://www.youtube.com/watch?v=_quPWFo7YPc">Breaking the cubic barrier in the Solovay-Kitaev algorithm</a>, QIP2023 video (2023).

%H J. C. Turner, <a href="https://www.fq.math.ca/Scanned/41-1/turner.pdf">Some fractals in goldpoint geometry</a>, The Fibonacci Quarterly, Vol. 41, No. 1 (2003), pp. 63-71.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals log(2) / log((sqrt(5)+1)/2).

%F Equals A002162/A002390. - _Amiram Eldar_, Nov 24 2020

%e 1.4404200904125564790175514995878638024586041426840560816454417295665...

%t RealDigits[Log[2]/Log[GoldenRatio], 10, 100][[1]] (* _Amiram Eldar_, Nov 24 2020 *)

%o (PARI) log(2)/log((sqrt(5)+1)/2) \\ _Charles R Greathouse IV_, May 15 2019

%Y Cf. A001622, A002162, A002390, A371176.

%K cons,nonn,easy

%O 1,2

%A Bryan Jacobs (bryanjj(AT)gmail.com), Feb 28 2005