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%I #9 Jun 08 2026 11:07:43
%S 8,9,8,5,1,9,4,1,8,2,6,6,1,1,8,8,5,6,2,7,7,8,6,3,2,4,2,0,3,5,3,8,4,3,
%T 3,3,9,7,2,9,3,3,1,4,6,4,3,2,8,1,5,7,6,0,8,5,1,8,1,7,6,0,8,6,4,8,8,9,
%U 6,1,7,3,8,2,1,1,8,4,1,0,8,0,3,6,1,8
%N Decimal expansion of Sum_{k>=0} cos(2k*Pi/5)/2^k.
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F Equals (49 + 3*sqrt(5))/62.
%F Equals Sum_{k>=0} cos(8 k*Pi/5)/2^k.
%F Minimal polynomial: 19 - 49 x + 31 x^2.
%F Equals 2 - 2*A373017. - _R. J. Mathar_, Aug 27 2024
%e 0.8985194182661188562778632420353843339729...
%t {b, m, h} = {2, 5, 2}; s = Sum[Cos[ h k Pi/m]/b^k, {k, 0, Infinity}]
%t d = N[s, 100]
%t First[RealDigits[d], 100]
%o (PARI) (49 + 3*sqrt(5))/62 \\ _Charles R Greathouse IV_, Jun 08 2026
%Y Cf. A373021 (includes guide to related sequences).
%Y Cf. A373017.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Jul 20 2024