A101689 Decimal expansion of the unique real number x whose Engel expansion is the Fibonacci sequence.

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

Offset: 1

Author

Ryan Propper, Dec 11 2004

Keywords

• cons
• nonn

Examples

			x = 2.70450289915406748719754896618187978517783483136...
		

Crossrefs

Cf. A000045, A137991 (reciprocal).

Programs

Mathematica

N[Sum[1/Product[Fibonacci[i], {i, n}], {n, 300}], 100]

PARI

suminf(n=1, 1/prod(i=1, n, fibonacci(i))) \\ Michel Marcus, Nov 28 2020

Formula

x = Sum_{n >= 1} 1/(Product_{1 <= i <= n} F(i)), where F(i) is the i-th Fibonacci number.