This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A073115 #31 Aug 21 2024 00:13:47
%S A073115 1,7,0,9,8,0,3,4,4,2,8,6,1,2,9,1,3,1,4,6,4,1,7,8,7,3,9,9,4,4,4,5,7,5,
%T A073115 5,9,7,0,1,2,5,0,2,2,0,5,7,6,7,8,6,0,5,1,6,9,5,7,0,0,2,6,4,4,6,5,1,2,
%U A073115 8,7,1,2,8,1,4,8,4,6,5,9,6,2,4,7,8,3,1,6,1,3,2,4,5,9,9,9,3,8,8,3,9,2,6,5,3
%N A073115 Decimal expansion of sum(k>=0, 1/2^floor(k*phi) ) where phi = (1+sqrt(5))/2.
%C A073115 Number whose digits are obtained from the substitution system (1->(1,0),0->(1)).
%C A073115 The n-th term of the continued fraction is 2^Fibonacci(n-2) (cf. A000301).
%C A073115 This number is known to be transcendental.
%D A073115 S. Wolfram, "A new kind of science", p. 913
%H A073115 J. L. Davison, <a href="http://www.jstor.org/stable/2041058">A series and its associated continued fraction</a>, Proc. Amer. Math. Soc. 63 (1977), pp. 29-32.
%H A073115 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A073115 Equals 1 + A014565.
%e A073115 1.70980344286129131464178739944457559701250220576786...
%t A073115 Take[ RealDigits[ Sum[N[1/2^Floor[k*GoldenRatio], 120], {k, 0, 300}]][[1]], 105] (* _Jean-François Alcover_, Jul 28 2011 *)
%o A073115 (PARI) phi=(1+sqrt(5))/2; suminf(n=0,2.^-(n*phi\1)) \\ _Charles R Greathouse IV_, Jul 22 2013
%o A073115 (PARI) phi=(1+sqrt(5))/2; suminf(n=1, (phi*n\1)/2^n) - 1 /* _Michael Somos_, May 22 2021 */
%K A073115 cons,nonn
%O A073115 1,2
%A A073115 _Benoit Cloitre_, Aug 19 2002