A103546 -id:A103546 - cp's OEIS frontend

A103616 Decimal expansion of the largest real root of the quintic equation x^5 + 2x^4 - 2x^3 - x^2 + 2*x -1 = 0.

7, 6, 6, 6, 0, 8, 6, 5, 4, 0, 7, 2, 8, 9, 1, 2, 0, 3, 7, 8, 3, 1, 8, 8, 4, 7, 2, 9, 8, 5, 2, 3, 0, 5, 9, 6, 7, 2, 1, 1, 4, 5, 4, 8, 5, 5, 4, 0, 5, 5, 5, 6, 7, 9, 4, 7, 1, 5, 5, 8, 0, 5, 0, 6, 2, 4, 5, 9, 6, 3, 0, 9, 1, 2, 9, 1, 6, 3, 5, 2, 8, 9, 0, 5, 6, 2, 7, 7, 4, 8, 3, 2, 9, 2, 2, 5, 6, 6, 1, 8, 8, 9, 6, 9, 8

Offset: 0

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 24 2005

See comments in A103546.

			0.76660865407289120......

Index entries for algebraic numbers, degree 5

Cf. A103546.

RealDigits[Root[x^5+2x^4-2x^3-x^2+2x-1,3],10,120][[1]] (* Harvey P. Dale, May 19 2019 *)

polrootsreal(x^5 + 2*x^4 - 2*x^3 - x^2 + 2*x -1)[3] \\ Charles R Greathouse IV, Apr 15 2014

A153122 G.f.: 1/p(x) where p(x)=x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1.

Original entry on oeis.org

1, -2, 6, -15, 38, -95, 237, -590, 1468, -3651, 9079, -22575, 56131, -139563, 347004, -862774, 2145156, -5333599, 13261165, -32971820, 81979285, -203828691, 506788203, -1260049698, 3132916721, -7789507968, 19367394583, -48154000782

Offset: 0

Roger L. Bagula and Gary W. Adamson, Dec 18 2008

a(n)/a(n-1) tends to the approximation to Feigenbaum's constant mentioned in A103546. = 2.48634376497....;.

Weisstein, Eric W. Feigenbaum Constant. Equation (11).
Index entries for linear recurrences with constant coefficients, signature (-2,2,1,-2,1).

Cf. A103546.

f[x_] = x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1;
g[x] = ExpandAll[x^5*f[1/x]]'
a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]

p(x)=x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1; a(n)=coefficient_expansion(1/(x^5*p(1/x))).

Edited by N. J. A. Sloane, Dec 19 2008

cp's OEIS Frontend

A103616 Decimal expansion of the largest real root of the quintic equation x^5 + 2x^4 - 2x^3 - x^2 + 2*x -1 = 0.

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A153122 G.f.: 1/p(x) where p(x)=x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1.

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cp's OEIS Frontend

A103616 Decimal expansion of the largest real root of the quintic equation x^5 + 2*x^4 - 2*x^3 - x^2 + 2*x -1 = 0.

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A153122 G.f.: 1/p(x) where p(x)=x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1.

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A103616 Decimal expansion of the largest real root of the quintic equation x^5 + 2x^4 - 2x^3 - x^2 + 2*x -1 = 0.