A390698 Decimal expansion of cos(5*Pi/33).

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for algebraic numbers, degree 10

Formula

Equals sin(23*Pi/66) = 2F1(-5/22,5/22;1/2;3/4) = -cos(28*Pi/33).

Second largest of the 10 real-valued roots of Product_{0<k<33 and k == 1 (mod 2) and gcd(k,33) = 1} 2*(cos(k*Pi/33) - x) = 1024*x^10 +512*x^9 -2560*x^8 -1280*x^7 +2176*x^6 +1088*x^5 -688*x^4 -344*x^3 +48*x^2 +24*x +1 =0.

Example

0.8888354486549234663115988929508545523678...

Mathematica

First[RealDigits[Cos[5*Pi/33], 10, 100]] (* Paolo Xausa, Nov 25 2025 *)

Prog

(PARI) cos(5*Pi/33)

Crossrefs

cos(k*Pi/33) = 2F1(-k/22.k/22;1/2;3/4): A387450 (k = 1), A387440 (k = 3), this sequence (k = 5), A390699 (k = 7), 1/2 (k = 11), -1/2 (k = 22), -A390699 (k = 26), -this (k = 28), -A387440 (k = 30), -A387450 (k = 32).

Cf. A389480.

Sequence in context: A023414 A125555 A010531 * A195141 A171811 A031176

Adjacent sequences: A390695 A390696 A390697 * A390699 A390700 A390701

Keyword

nonn,cons,easy

Author

A.H.M. Smeets, Nov 15 2025

Status

approved