A371648 - OEIS

%I #6 Jan 05 2025 19:51:42

%S 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,

%T 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,

%U 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

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

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

%H M. A. Nyblom, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-4/quartnyblom04_2004.pdf">On the Construction of a Family of Transcendental Valued Infinite Products</a>, Fibonacci Quarterly, Vol. 42, No. 4 (2004), pp. 353-358.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

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

%e 2.40003198933688770409863382912459044885549783193387...

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

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

%Y Cf. A000045, A145232, A371647.

%Y Similar constants: A337668, A337669, A371650.

%K nonn,cons

%O 1,1

%A _Amiram Eldar_, Mar 31 2024