A348909 - OEIS

%I #7 Nov 19 2021 08:12:38

%S 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,

%T 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,

%U 6,8,0,2,0,7,8,0,3,3,6,0,7,4,8,4,4,2,9,0,7,8

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

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

%H Daniel J. Katz and Courtney M. van der Linden, <a href="https://arxiv.org/abs/2108.07318">Peak Sidelobe Level and Peak Crosscorrelation of Golay-Rudin-Shapiro Sequences</a>, arXiv:2108.07318 [cs.IT], 2021. See Theorems 1.3, 1.4 and 1.5, pp. 4-5.

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

%e 1.6589670819169940793467751567840...

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

%o (PARI) solve(x=0, 2, x^3 + x^2 - 2*x - 4) \\ _Michel Marcus_, Nov 03 2021

%Y Cf. A020985, A020987, A348908.

%K nonn,cons

%O 1,2

%A _Stefano Spezia_, Nov 03 2021