A160155 -id:A160155 - cp's OEIS frontend

A358942 Decimal expansion of the real root of x^5 - x^2 - 1.

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

Offset: 1

Wolfdieter Lang, Dec 15 2022

The other (complex) roots are 0.154589676718332223... + 0.828074133201299911...*i, and -0.751519232378943729... + 0.784615921039447991...*i, together with their conjugates.

			1.19385911132122301200902074629803112451452426948644450960208140159603556...

Cf. A160155, A230152, A358939, A358940, A358941.

RealDigits[x /. FindRoot[x^5 - x^2 - 1, {x, 1}, WorkingPrecision -> 120], 10, 120][[1]] (* Amiram Eldar, Dec 15 2022 *)

A039922 Continued fraction for root of x^5 - x - 1.

Original entry on oeis.org

1, 5, 1, 42, 1, 3, 24, 2, 2, 1, 16, 1, 11, 1, 1, 2, 31, 1, 12, 5, 1, 7, 11, 1, 4, 1, 4, 2, 2, 3, 4, 2, 1, 1, 11, 1, 41, 12, 1, 8, 1, 1, 1, 1, 1, 9, 2, 1, 5, 4, 1, 25, 4, 6, 11, 1, 4, 1, 6, 1, 1, 1, 2, 2, 2, 4, 11, 1, 4, 1, 3, 2, 8, 1, 3, 3, 6, 21, 11, 2, 1, 1, 10, 2, 1, 3

Offset: 0

N. J. A. Sloane

			1.16730397826141868425604589... = 1 + 1/(5 + 1/(1 + 1/(42 + 1/(1 + ...)))).

Harry J. Smith, Table of n, a(n) for n = 0..20000
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]
G. Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A160155 Decimal expansion.

{ allocatemem(932245000); default(realprecision, 21000); x=NULL; p=x^5 - x - 1; rs=polroots(p); r=real(rs[1]); c=contfrac(r); for (n=1, 20001, write("b039922.txt", n-1, " ", c[n])); } \\ Harry J. Smith, May 03 2009

contfrac(polrootsreal(x^5-x-1)[1]) \\ Charles R Greathouse IV, Apr 14 2014

A301509 Decimal expansion of (1 + (1 + (1 + (1 + ...)^(1/5))^(1/4))^(1/3))^(1/2).

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Mar 22 2018

			1.517600167877718891370658043063416271885...

Eric Weisstein's World of Mathematics, Nested Radical

Cf. A001622, A060006, A060007, A160155, A296547.

cp's OEIS Frontend

A358942 Decimal expansion of the real root of x^5 - x^2 - 1.

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A039922 Continued fraction for root of x^5 - x - 1.

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A301509 Decimal expansion of (1 + (1 + (1 + (1 + ...)^(1/5))^(1/4))^(1/3))^(1/2).

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