A348909 Decimal expansion of the real root of x^3 + x^2 - 2*x - 4.

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

Offset: 1

Author

Stefano Spezia, Nov 03 2021

Keywords

• nonn
• cons

Comments

This constant appears in the upper bounds formula of both the peak sidelobe level and the peak cross-correlation of Rudin-Shapiro sequences.

Examples

			1.6589670819169940793467751567840...
		

Links

• Daniel J. Katz and Courtney M. van der Linden, Peak Sidelobe Level and Peak Crosscorrelation of Golay-Rudin-Shapiro Sequences, arXiv:2108.07318 [cs.IT], 2021. See Theorems 1.3, 1.4 and 1.5, pp. 4-5.

Crossrefs

Cf. A020985, A020987, A348908.

Programs

Mathematica

First[RealDigits[N[Root[x^3+x^2-2x-4,x,1],90]]]

PARI

solve(x=0, 2, x^3 + x^2 - 2*x - 4) \\ Michel Marcus, Nov 03 2021

Formula

Equals ((44 + 3*sqrt(177))^(1/3) + (44 - 3*sqrt(177))^(1/3) - 1)/3.