A371648 Decimal expansion of Product_{k>=0} (1 + 1/Fibonacci(5^k)).

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

Offset: 1

Author

Amiram Eldar, Mar 31 2024

Keywords

• nonn
• cons

Comments

This constant is a transcendental number (Nyblom, 2004).

Examples

			2.40003198933688770409863382912459044885549783193387...
		

Links

• M. A. Nyblom, On the Construction of a Family of Transcendental Valued Infinite Products, Fibonacci Quarterly, Vol. 42, No. 4 (2004), pp. 353-358.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000045, A145232, A371647.

Similar constants: A337668, A337669, A371650.

Programs

Mathematica

RealDigits[Product[1 + 1/Fibonacci[5^k], {k, 0, 10}], 10, 120][[1]]

PARI

prodinf(k = 0, 1 + 1/fibonacci(5^k))

Formula

Equals Product_{k>=0} (1 + 1/A145232(k)).