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 A373785 #30 Jun 27 2024 22:26:41
%S A373785 2,2,2,3,4,5,9,8,3,0,0,0,7,1,3,0,1,0,7,8,5,4,5,7,7,0,1,8,7,4,4,7,9,9,
%T A373785 4,7,3,3,0,7,0,5,6,9,0,9,1,3,7,1,3,8,3,2,7,3,1,4,3,6,7,1,8,5,6,3,8,0,
%U A373785 1,5,5,4,4,5,1,1,1,6,6,7,6,7,8,1,3,1,5,3,7,8,7,6,3,9,5,8,8,5,6,5,9,4,1
%N A373785 Decimal expansion of the area of the Spiral of Theodorus.
%C A373785 The length of the legs of the k-th triangle of the Spiral of Theodorus are 1 and sqrt(k), while the length of the hypotenuse is sqrt(k + 1). Theodorus stopped at the 16th triangle, whose hypotenuse measures sqrt(17), because from the next triangle his spiral began to overlap (see A072895).
%C A373785 The area of the k-th triangle is (1/2) * sqrt(k), so the area A of the spiral constructed by Theodorus is A = (1/2)*Sum_{k=1..16} sqrt(k) = 22.234598300071...
%C A373785 The perimeter of the spiral of Theodorus (up to the 16th triangle) is 17 + sqrt(17).
%H A373785 Wikipedia, <a href="https://en.wikipedia.org/wiki/Spiral_of_Theodorus">Spiral of Theodorus</a>.
%F A373785 Equals (1/2)*Sum_{k=1..16} sqrt(k).
%e A373785 22.234598300071301078545770187447994733070569...
%t A373785 RealDigits[(1/2)*Sum[Sqrt[k],{k,16}],10,120][[1]] (* _Stefano Spezia_, Jun 23 2024 *)
%Y A373785 Cf. A072895.
%K A373785 nonn,cons
%O A373785 1,1
%A A373785 _Gonzalo MartÃnez_, Jun 23 2024