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 A068521 #45 Apr 28 2025 07:08:06 %S A068521 1,4,5,6,7,9,1,0,3,1,0,4,6,9,0,6,8,6,9,1,8,6,4,3,2,3,8,3,2,6,5,0,8,1, %T A068521 9,7,4,9,7,3,8,6,3,9,4,3,2,2,1,3,0,5,5,9,0,7,9,4,1,7,2,3,8,3,2,6,7,9, %U A068521 2,6,4,5,4,5,8,0,2,5,0,9,0,0,2,5,7,4,7,3,7,1,2,8,1,8,4,4,8,4,4,4,3,2,8,1,8 %N A068521 Decimal expansion of agm(1, 2). %C A068521 This is the arithmetic-geometric mean of 1 and 2, given by u(1) = 1, v(1) = 2, u(n+1) = (u(n)+v(n))/2, v(n+1) = sqrt(u(n)*v(n)); agm(1,2) = lim u(n) = lim v(n). %C A068521 Schneider proved that this constant is transcendental. - _Charles R Greathouse IV_, Feb 03 2025 %H A068521 Ivan Panchenko, <a href="/A068521/b068521.txt">Table of n, a(n) for n = 1..1000</a> %H A068521 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Arithmetic-GeometricMean.html">Arithmetic-Geometric Mean</a>. %H A068521 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean">Arithmetic-geometric mean</a>. %H A068521 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>. %F A068521 Equals Pi/EllipticK(3/4) = A000796 / A249283. - _Amiram Eldar_, Apr 28 2025 %e A068521 1.45679103104690686918643238326508197497386394322130559079417238326792645458025... %p A068521 evalf(GaussAGM(1, 2), 144); # _Alois P. Heinz_, Jul 05 2023 %p A068521 evalf(Pi/EllipticK(sqrt(3)/2), 107); # or %p A068521 evalf(3*Pi/(4*EllipticK(1/3)), 107); # _Vaclav Kotesovec_, Mar 28 2024 %t A068521 RealDigits[ ArithmeticGeometricMean[1, 2], 10, 107] // First (* _Jean-François Alcover_, Feb 06 2013 *) %t A068521 RealDigits[N[3Pi/(4EllipticK[1/9]), 107]][[1]] (* _Jean-François Alcover_, Jun 02 2019 *) %t A068521 RealDigits[N[Pi/EllipticK[3/4], 107]][[1]] (* or *) %t A068521 RealDigits[N[Pi/(2*EllipticK[-3]), 107]][[1]] (* _Vaclav Kotesovec_, Mar 28 2024 *) %o A068521 (PARI) agm(1,2) \\ _Charles R Greathouse IV_, Mar 03 2016 %Y A068521 Cf. A084895 (agm(1,3)), A084896 (agm(1,4)), A084897 (agm(1,5)), A000796, A249283. %K A068521 easy,nonn,cons %O A068521 1,2 %A A068521 _Benoit Cloitre_, Mar 21 2002