A119801 Decimal representation of continued fraction 1, 1, 2, 3, 5, 8, 13 ... (Fibonacci[n]).

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

Offset: 1

Author

Alexander Adamchuk, Jul 30 2006

Keywords

• nonn
• cons

Comments

C = 1.6981562788972284466931540436689336838294864493643766226750196575685068035717\

02408583262343394744820209675493364365510752097635919...

C is a limit of A026822[n]/A071895[n+1] = {1, 2, 5/3, 17/10, 90/53, 737/434, 9671/5695, 203828/120029, 6939823/4086681, ...} = (1 + 1/(1 + 1/(2 + 1/(3 + 1/(5 + 1/(8 + 1/(13 + 1/(21 + 1/(34 + 1/(55 + ...

Crossrefs

Cf. A026822, A071895, A000045.

Cf. A073822 (reciprocal).

Programs

Mathematica

RealDigits[ Normal[ ContinuedFractionForm[ Table[ Fibonacci[k],{k,1,30}] ]], 10, 130] [[1]]

Formula

a(n) = limit[ A026822[n]/A071895[n+1], n->Infinity].

Extensions

Definition corrected by T. D. Noe, May 19 2007