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 A196522 #32 Oct 23 2024 01:02:23
%S A196522 9,4,8,0,5,9,4,4,8,9,6,8,5,1,9,9,3,5,6,8,4,8,1,5,5,4,6,6,6,7,5,2,4,5,
%T A196522 7,2,8,5,1,4,7,3,8,8,6,0,9,3,8,4,9,5,0,5,5,0,7,5,4,2,5,2,4,9,0,8,0,3,
%U A196522 1,3,9,9,9,2,3,2,1,0,3,6,3,6,5,0,4,2,0,2,2,0,0,1,3,3,6,0,2,8
%N A196522 Decimal expansion of Pi*(1+sqrt(2))/8.
%C A196522 This is the mean of two Dirichlet L=functions modulo m=8 at s=1, one with character (1,0,-1,0,1,0,-1,0) as in A101455, the other with character (1,0,1,0,-1,0,-1,0).
%C A196522 The area of a circle circumscribed in a unit-area regular octagon. - _Amiram Eldar_, Nov 05 2020
%D A196522 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.4.1, p. 20.
%D A196522 L. B. W. Jolley, Summation of series, Dover (1961), eq. 78 page 16 and eq. 264 page 48.
%H A196522 G. C. Greubel, <a href="/A196522/b196522.txt">Table of n, a(n) for n = 0..10000</a>
%H A196522 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A196522 Equals (1 - 1/7) + (1/9 - 1/15) + ... + (1/(1+8*k) - 1/(7+8*k)) + ... = (A093954 + A003881)/2.
%F A196522 Equals Sum_{n >= 0} (8*k + 6)/((8*n + 1)*(8*n + 8*k + 7)) - Sum_{n = 0..k-1} 1/(8*n + 7), for positive integer k. - _Peter Bala_, Jul 10 2024
%e A196522 0.948059448968519935684815...
%t A196522 RealDigits[Pi*(1+Sqrt[2])/8,10,120][[1]] (* _Harvey P. Dale_, May 31 2013 *)
%o A196522 (PARI) default(realprecision, 100); Pi*(1+sqrt(2))/8 \\ _G. C. Greubel_, Oct 05 2018
%o A196522 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*(1+Sqrt(2))/8; // _G. C. Greubel_, Oct 05 2018
%K A196522 nonn,cons,easy
%O A196522 0,1
%A A196522 _R. J. Mathar_, Oct 03 2011