A226765 Decimal expansion of (13-5*sqrt(5))/2.

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

Offset: 0

Author

Clark Kimberling, Jul 21 2013

Keywords

• nonn
• cons
• easy

Comments

(13 - 5*sqrt(5))/2 = lim_{n->oo} -F(n)+(2+F(n+1))*(1+F(n+2))/(3+F(n+3)), where F = A000045 (Fibonacci numbers).

Apart from leading digits the same as A187798 and A187426. - R. J. Mathar, Sep 21 2013

Examples

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

Links

• Clark Kimberling, Table of n, a(n) for n = 0..999

Crossrefs

Cf. A000045, A187426, A187798, A225667.

Programs

Mathematica

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]]