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 A020797 #44 Feb 04 2025 10:58:51 %S A020797 1,5,8,1,1,3,8,8,3,0,0,8,4,1,8,9,6,6,5,9,9,9,4,4,6,7,7,2,2,1,6,3,5,9, %T A020797 2,6,6,8,5,9,7,7,7,5,6,9,6,6,2,6,0,8,4,1,3,4,2,8,7,5,2,4,2,6,3,9,6,2, %U A020797 9,7,2,1,9,3,1,9,6,1,9,1,1,0,6,7,2,1,2,4,0,5,4,1,8,9,6,5,0,1,4 %N A020797 Decimal expansion of 1/sqrt(40). %C A020797 With offset 1, decimal expansion of sqrt(5/2). - _Eric Desbiaux_, May 01 2008 %C A020797 sqrt(5/2) appears as a coordinate in a degree-5 integration formula on 13 points in the unit sphere [Stroud & Secrest]. - _R. J. Mathar_, Oct 12 2011 %C A020797 With offset 2, decimal expansion of sqrt(250). - _Michel Marcus_, Nov 04 2013 %C A020797 From _Wolfdieter Lang_, Nov 21 2017: (Start) %C A020797 The regular continued fraction of 1/sqrt(40) = 1/(2*sqrt(10)) is [0; 6, 3, repeat(12, 3)], and the convergents are given by A(n-1)/B(n-1), n >= 0, with A(-1) = 0, A(n-1) = A041067(n) and B(-1) = 1, B(n-1) = A041066(n). %C A020797 The regular continued fraction of sqrt(5/2) = sqrt(10)/2 is [1; repeat(1, 1, 2)], and the convergents are given in A295333/A295334. %C A020797 sqrt(10)/2 is one of the catheti of the rectangular triangle with hypotenuse sqrt(13)/2 = A295330 and the other cathetus sqrt(3)/2 = A010527. This can be constructed from a regular hexagon inscribed in a circle with a radius of 1 unit. If the vertex V_0 has coordinates (x, y) = (1, 0) and the midpoint M_4 = (0, -sqrt(3)/2) then the point L = (sqrt(10)/2, 0) is obtained as intersection of the x-axis and a circle around M_4 with radius taken from the distance between M_4 and V_1 = (1/2, sqrt(3)/2) which is sqrt(13)/2. (End) %H A020797 Ivan Panchenko, <a href="/A020797/b020797.txt">Table of n, a(n) for n = 0..1000</a> %H A020797 A. H. Stroud, D. Secrest, <a href="http://dx.doi.org/10.1090/S0025-5718-1963-0161473-0">Approximate integration formulas for certain spherically symmetric regions</a>, Math. Comp. 17 (82) (1963) 105. %H A020797 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>. %F A020797 Equals Re(sqrt(5*i)/10) = Im(sqrt(5*i)/10). - _Karl V. Keller, Jr._, Sep 01 2020 %F A020797 Equals A010467/20. - _R. J. Mathar_, Feb 23 2021 %e A020797 1/sqrt(40) = 0.15811388300841896659994467722163592668597775696626084134287... %e A020797 sqrt(5/2) = 1.5811388300841896659994467722163592668597775696626084134287... %e A020797 sqrt(250) = 15.811388300841896659994467722163592668597775696626084134287... %t A020797 RealDigits[N[1/Sqrt[40],200]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 01 2010 *) %o A020797 (PARI) 1/sqrt(40) \\ _Charles R Greathouse IV_, Feb 04 2025 %o A020797 (PARI) polrootsreal(40*x^2-1)[2] \\ _Charles R Greathouse IV_, Feb 04 2025 %Y A020797 Cf. A010467 (sqrt(10)), A010527, A010494 (sqrt(40)), A041067/A041066, A295330, A295333/A295334. %K A020797 nonn,cons %O A020797 0,2 %A A020797 _N. J. A. Sloane_