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 A193720 Decimal expansion of Burnside curve length. 1
 3, 8, 7, 8, 5, 5, 4, 8, 5, 8, 7, 4, 1, 0, 5, 6, 1, 8, 1, 0, 6, 6, 0, 8, 0, 1, 0, 8, 2, 1, 8, 8, 5, 0, 6, 4, 9, 6, 3, 6, 4, 5, 7, 8, 4, 5, 6, 5, 8, 1, 1, 9, 1, 2, 1, 4, 8, 3, 7, 6, 3, 7, 8, 3, 0, 7, 0, 9, 2, 8, 9, 6, 0, 0, 1, 9, 7, 0, 1, 5, 1, 4, 7, 4, 0, 5, 2, 3, 9, 2, 5, 5, 5, 6, 3, 7, 2, 0, 2, 1, 7, 5, 9, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..105. Eric Weisstein's World of Mathematics, Burnside Curve EXAMPLE 3.878554858741... MATHEMATICA f[x_, y_] = y^2 - x (x^4 - 1); f[x_] = Sqrt[-x + x^5]; x1 = -5/6; y1 = f[x1]; x2 = -1/4; y2 = f[x2]; eq = Eliminate[f[g[y], y] == 0 && D[f[g[y], y], y] == 0, g[y]]; dg1[y_] = g'[y] /. Solve[eq, g'[y]][[3]]; dg2[y_] = g'[y] /. Solve[eq, g'[y]][[1]]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Sqrt[1 + dg1[y]^2], {y, 0, y1}]; i2 = ni[Sqrt[1 + f'[x]^2], {x, x1, x2}]; i3 = ni[Sqrt[1 + dg2[y]^2], {y, 0, y2}]; Take[RealDigits[2(i1+i2+i3)][[1]], 105] CROSSREFS Cf. A193719 (area). Sequence in context: A106043 A294833 A202478 * A011255 A342664 A101297 Adjacent sequences: A193717 A193718 A193719 * A193721 A193722 A193723 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Aug 03 2011 EXTENSIONS Mathematica program simplified by Jean-François Alcover, Aug 26 2011 STATUS approved

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Last modified November 28 05:36 EST 2023. Contains 367394 sequences. (Running on oeis4.)