A371322 Decimal expansion of Sum_{k>=1} 1/(2^k * Fibonacci(k!)).

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

Offset: 0

Author

Amiram Eldar, Mar 19 2024

Keywords

• nonn
• cons

Comments

The transcendence of this constant was proved by Nyblom (2001).

Examples

			0.76562634791235334713595583744001463296000771662912...
		

Links

• M. A. Nyblom, A Theorem on Transcendence of Infinite Series II, Journal of Number Theory, Vol. 91, No. 1 (2001), pp. 71-80.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000045, A000142, A063374, A343202, A371323, A371324, A371325.

Programs

Mathematica

RealDigits[Sum[1/(2^k * Fibonacci[k!]), {k, 1, 10}], 10, 120][[1]]

PARI

suminf(k = 1, 1/(2^k * fibonacci(k!)))