A371650 Decimal expansion of Product_{k>=0} (1 + 1/Lucas(5^k)).

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

Offset: 1

Author

Amiram Eldar, Mar 31 2024

Keywords

• nonn
• cons

Comments

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

Examples

			2.18183118733306202384236017055676106780243564695796...
		

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. A000032, A144837, A371649.

Similar constants: A371525, A371526, A371648.

Programs

Mathematica

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

PARI

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

Formula

Equals Product_{k>=0} (1 + 1/A144837(k)).