A395138 Decimal expansion of the absolute value of the real part of the complex roots of x^3 - x^2 - 1 = 0.

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

Offset

0,1

Comments

The three roots of x^3 - x^2 - 1 = 0 are A092526, -A395138 + i*A395139 and -A395138 - i*A395139, where i = sqrt(-1).

Links

Table of n, a(n) for n=0..87.

Jeffrey Shallit, The Narayana Morphism and Related Words, arXiv:2503.01026 [math.CO], 2025.

Index entries for algebraic numbers, degree 3

Formula

Equals (A092526 - 1)/2.

Equals A088559/2.

Equals A263719^2/2.

Unique real root to 8*x^3 + 8*x^2 + 2*x - 1 = 0. - Jianing Song, Apr 23 2026

Example

0.23278561593838401332836561260996955401278878423614285082...

Mathematica

RealDigits[Re[2/3*Cos[ArcCos[29/2]/3-2*Pi/3]+1/3], 10, 88][[1]] (* Stefano Spezia, Apr 17 2026 *)

Prog

(PARI) -real(2/3*cos(acos(29/2)/3-2*Pi/3)+1/3)
(PARI) solve(x=0, 1, 8*x^3 + 8*x^2 + 2*x - 1) \\ Jianing Song, Apr 23 2026

Crossrefs

Cf. A088559, A092526, A263719, A395139.

Sequence in context: A208930 A122076 A209774 * A271322 A373420 A170842

Adjacent sequences: A395135 A395136 A395137 * A395139 A395140 A395141

Keyword

nonn,cons

Author

A.H.M. Smeets, Apr 13 2026

Status

approved