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%I #5 Mar 19 2024 10:28:52
%S 2,6,5,6,2,3,6,5,2,0,8,7,6,4,6,6,5,2,8,6,4,0,4,4,1,7,4,2,2,4,0,0,3,5,
%T 9,0,8,6,2,0,0,9,0,9,6,8,9,1,3,7,5,5,5,7,4,3,0,4,7,3,3,0,7,3,1,3,1,1,
%U 5,8,0,8,3,1,3,8,2,0,5,2,5,9,3,8,2,7,4,8,9,5,9,5,3,3,6,3,7,1,0,6,9,4,3,2,5
%N Decimal expansion of Sum_{k>=1} (-1)^(k+1)/(2^k * Fibonacci(k!)).
%C The transcendence of this constant was proved by Nyblom (2004).
%H M. A. Nyblom, <a href="https://doi.org/10.1016/j.jnt.2003.09.005">An extension of a result of Sierpiński</a>, Journal of Number Theory, Vol. 105, No. 1 (2004), pp. 49-59.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e 0.26562365208764665286404417422400359086200909689137...
%t RealDigits[-Sum[(-1/2)^k/Fibonacci[k!], {k, 1, 10}], 10, 120][[1]]
%o (PARI) suminf(k = 1, -(-1/2)^k/fibonacci(k!))
%Y Cf. A000045, A000142, A063374, A343202, A371322, A371323, A371325.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Mar 19 2024