A390698 - OEIS

%I #24 Nov 26 2025 19:26:13

%S 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,

%T 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,

%U 1,0,4,1,8,8,8,0,6,1,6,6,9,1,7,0,8,3,0

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

%H Paolo Xausa, <a href="/A390698/b390698.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Al#algebraic_10">Index entries for algebraic numbers, degree 10</a>

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

%F 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.

%e 0.8888354486549234663115988929508545523678...

%t First[RealDigits[Cos[5*Pi/33], 10, 100]] (* _Paolo Xausa_, Nov 25 2025 *)

%o (PARI) cos(5*Pi/33)

%Y 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).

%Y Cf. A389480.

%K nonn,cons,easy

%O 0,1

%A _A.H.M. Smeets_, Nov 15 2025