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Decimal expansion of (13-5*sqrt(5))/2.
5

%I #13 Jan 17 2018 17:12:19

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

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

%U 7,6,8,5,9,0,5,4,8,7,7,5,1,4,6,3,9,6

%N Decimal expansion of (13-5*sqrt(5))/2.

%C (13 - 5*sqrt(5))/2 = limit of -F(n)+(2+F(n+1))(1+F(n+2)))/(3+F(n+3)), where F = A000045 (Fibonacci numbers).

%C Apart from leading digits the same as A187798 and A187426. - _R. J. Mathar_, Sep 21 2013

%H Clark Kimberling, <a href="/A226765/b226765.txt">Table of n, a(n) for n = 0..999</a>

%e (13-5*sqrt(5))/2 = 0.9098300562505257589770658281718094113985...

%t f[n_] := Fibonacci[n]; h[n_] := (2 + f[n + 1]) (1 + f[n + 2])/(3 + f[n + 3]); N[h[100] - f[100], 20]; d = RealDigits[(13 - 5*Sqrt[5])/2, 10, 120][[1]]

%Y Cf. A000045, A225667.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Jul 21 2013