A358945 Decimal expansion of the positive root of 4*x^2 + x - 1.

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

Offset

0,1

Comments

The negative root is -(A189038 - 1) = -0.6403882032... .

c^n = A052923(-n) + A006131(-(n+1))*phi17, for n >= 0, with phi17 = A222132 = (1 + sqrt(17))/2, A052923(-n) = -(-2*i)^(-n)*S(-(n+2), i/2) = (i/2)^n*S(n, i/2), with i = sqrt(-1), and A006131(-(n+1)) = A052923(-n+1)/4 = -(i/2)^(n+1)*S(n-1, i/2), with the S-Chebyshev polynomials (see A049310), and S(-n, x) = -S(n-2, x), for n >= 1. - Wolfdieter Lang, Jan 04 2024

Links

Table of n, a(n) for n=0..75.

Index entries for sequences related to Chebyshev polynomials.

Formula

c = (-1 + sqrt(17))/8 = A189038 - 5/4 = A174930 - 5/8.

c = 1/phi17 = (-1 + phi17)/4, with phi17 = A222132. - Wolfdieter Lang, Jan 05 2024

Example

c = 0.39038820320220756872767623199675962814339990317170255429982919663...

Mathematica

RealDigits[(Sqrt[17] - 1)/8, 10, 120][[1]] (* Amiram Eldar, Jan 20 2023 *)
RealDigits[Root[4x^2+x-1, 2], 10, 120][[1]] (* Harvey P. Dale, Jan 15 2024 *)

Crossrefs

Cf. A006131, A010473, A049310, A052923, A174930, A189038, A222132.

Sequence in context: A016626 A126321 A335777 * A248726 A267411 A370468

Adjacent sequences: A358942 A358943 A358944 * A358946 A358947 A358948

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, Jan 20 2023

Status

approved