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 A328227 #43 Jun 30 2022 09:09:01 %S A328227 4,6,0,3,3,3,8,8,4,8,7,5,1,7,0,0,3,5,2,5,5,6,5,8,2,0,2,9,1,0,3,0,1,6, %T A328227 5,1,3,0,6,7,3,9,7,1,3,4,1,6,0,5,3,2,3,4,6,0,3,9,4,3,0,1,1,5,4,3,8,4, %U A328227 5,8,7,3,1,9,6,5,9,7,0,9,9,8,7,1,6,5,4,6,9,9,7,2,2,7,2 %N A328227 Decimal expansion of positive solution to x^2 = 1 + (Pi + arccos(1/x))^2. %C A328227 We are in a rowboat on a circular lake, starting at the center. At the edge of the lake is a mean goblin. He can run k times as fast as we can row. This is the minimum value of k such that we will not be able to escape. %C A328227 From _Rian Hunter_, Jun 16 2021: (Start) %C A328227 For a spirograph defined by complex function z = p * e^(-i * b * t) + b * e^(i * t), this is the value of p as b->oo such that each petal is tangent to the next one. %C A328227 If we consider the set of all right triangles such that their tangent value is equal to the opposite angle in radians, this value is equal to the negative secant of the right triangle from that set with the smallest nonzero opposite angle. (End) %C A328227 The envelope of the t*x = sin(t*y) family of curves contains the set of y = (-1)^n*k_n*x straight lines (n > 0), where k_n is the solution of (n*Pi + arccos(1/k))^2 + 1 = k^2. This entry is k_1. See illustration, section Links. - _Luc Rousseau_, Mar 11 2022 %C A328227 Maximum negative value of x/sin(x). - _Andrew Slattery_, Jun 29 2022 %H A328227 Rian Hunter, <a href="https://thelig.ht/petalnumbers/part2.html">The Number Hiding Inside the Spirograph</a>. %H A328227 IBM Research, <a href="https://www.research.ibm.com/haifa/ponderthis/challenges/May2001.html">Ponder This Challenge - May 2001</a>. %H A328227 Luc Rousseau, <a href="/A328227/a328227.png">A328227 viewed as the |slope| of an envelope</a>. %F A328227 x=-sec(y), where decimal expansion of y is A115365. %F A328227 Alternatively, x=sqrt(y^2+1). %e A328227 4.6033388487517003525565820291030165130673971341605323460394301154384587319659... %t A328227 NSolve[x^2==1+(Pi+ArcCos[1/x])^2,x,Reals,WorkingPrecision->100] %o A328227 (PARI) solve(x=4, 5, 1 + (Pi+acos(1/x))^2 - x^2) \\ _Michel Marcus_, Oct 08 2019 %Y A328227 Cf. A115365. %Y A328227 Equals 1/A213053. %K A328227 nonn,cons %O A328227 1,1 %A A328227 _Jack Zhang_, Oct 08 2019