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 A235063 #13 Jun 27 2023 15:07:58 %S A235063 2,2,4,2,8,3,8,1,8,3,4,2,12,2,8,1,8,3,4,2,8,3,8,1,12,2,4,2,12,2,8,1,8, %T A235063 3,4,2,8,3,8,1,8,3,4,2,12,2,8,1,12,2,4,2,8,3,8,1,12,2,4,2,12,2,8,1,8, %U A235063 3,4,2,8,3,8,1,8,3,4,2,12,2,8,1,8,3,4,2,8,3,8,1,12,2,4,2,12,2,8,1,12,2,4 %N A235063 Continued fraction expansion of Sum(i=1..inf, 1/2^(2^i+1) ). %H A235063 H. Cohn, <a href="http://arXiv.org/abs/math.NT/0008221">Symmetry and specializability in continued fractions</a>. arXiv preprint math/0008221 (2000), published in Acta Arithmetica 75 (1996): 4. %H A235063 Jeffrey Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Papers/scf.pdf">Simple continued fractions for some irrational numbers</a>, J. Number Theory 11 (1979), no. 2, 209-217. %H A235063 <a href="/index/Con#confC">Index entries for continued fractions for constants</a> %F A235063 0.40821075451094657... = (1/2) A007400. %F A235063 Recurrence: a(8n)=1, a(8n+4)=a(16n+14)=a(32n+26)=2, a(16n+6)=a(32n+10)=3, a(8n+3)=4, a(8n+7)=a(16n+5)=a(32n+9)=8, a(16n+13)=a(32n+25)=12, a(8n+1)=a(4n+1), a(8n+2)=a(4n+2), starting 2,2,4 (conjectured). %e A235063 0.40821075451094657... = 2/(2+1/(2+1/(4+1/(2+1/(8+1/(3+1/8... %o A235063 (PARI) a(n)=contfrac(suminf(i=0, 1/2^(2^i+1)))[n+1] %Y A235063 Cf. A007400. %K A235063 cofr,nonn %O A235063 0,1 %A A235063 _Ralf Stephan_, Jan 03 2014