A348908 Decimal expansion of the positive real root of x^4 - 3*x - 6.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..89.

Tom Høholdt, Helge Elbrønd Jensen and Jørn Justesen, Aperiodic correlations and the merit factor of a class of binary sequences (Corresp.), in IEEE Transactions on Information Theory, vol. 31, no. 4, pp. 549-552, July 1985; on Research Gate.

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 Theorem 1.2, p. 4.

Stefano Spezia, Exact form of the constant

Formula

See the formula in Links section.

Example

1.8426267135838135939675706175443422...

Mathematica

First[RealDigits[N[Root[x^4-3x-6, x, 2], 89]]]

Prog

(PARI) solve(x=0, 2, x^4 - 3*x - 6) \\ Michel Marcus, Nov 03 2021

Crossrefs

Cf. A020985, A020987, A348909.

Sequence in context: A198353 A010523 A231534 * A014391 A099286 A089729

Adjacent sequences: A348905 A348906 A348907 * A348909 A348910 A348911

Keyword

nonn,cons

Author

Stefano Spezia, Nov 03 2021

Status

approved