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 A236145 #8 Sep 04 2023 17:41:18
%S A236145 1,10,14,124,2039,262111,536870655,140737488347135,
%T A236145 75557863725914321321983,10633823966279326983230456465062887423,
%U A236145 803469022129495137770981046170581301261101460862599398686719
%N A236145 Records in the continued fraction expansion of Sum_{k >= 2} 2^(-Fibonacci(k)) (A006518).
%C A236145 Positions of records are at 2, 7, 9, 13, 19, 27, 35, 47, 63, 87, 117, 159, 217, 301, 413, ...
%F A236145 Conjecture: For n>4, a(n) = 2^L(n) - 2^F(n) - 1, with L(n) the Lucas numbers A000032, and F(n) the Fibonacci numbers.
%t A236145 Rest[DeleteDuplicates[ContinuedFraction[Sum[2^-Fibonacci[k],{k,2,20}]],GreaterEqual]] (* _Harvey P. Dale_, Sep 04 2023 *)
%o A236145 (PARI) m=1;for(n=1,500,t=contfrac(suminf(i=2, 1/2^fibonacci(i)))[n+1];if(m<t,m=t;print1(t,",")))
%K A236145 nonn
%O A236145 1,2
%A A236145 _Ralf Stephan_, Jan 19 2014