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%I #8 Mar 31 2024 08:43:41
%S 1,0,9,0,9,1,5,0,5,1,7,7,0,0,7,7,6,7,0,0,1,8,6,5,7,5,0,2,4,1,4,2,2,8,
%T 2,0,5,7,1,5,1,7,5,1,0,2,3,1,9,9,0,6,6,9,8,9,0,5,0,3,2,1,7,0,9,2,2,2,
%U 4,3,0,8,1,7,5,8,2,8,8,4,4,6,4,9,0,2,6,3,1,9,6,7,3,7,2,4,8,1,8,3,1,2,4,1,7
%N Decimal expansion of Sum_{k>=0} 1/Lucas(5^k).
%C This constant is a transcendental number (Nyblom, 2001).
%H M. A. Nyblom, <a href="https://doi.org/10.1006/jnth.2001.2672">A Theorem on Transcendence of Infinite Series II</a>, Journal of Number Theory, Vol. 91, No. 1 (2001), pp. 71-80.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F Equals Sum_{k>=0} 1/A144837(k).
%e 1.09091505177007767001865750241422820571517510231990...
%t RealDigits[Sum[1/LucasL[5^k], {k, 0, 10}], 10, 120][[1]]
%o (PARI) suminf(k = 0, 1/(fibonacci(5^k-1) + fibonacci(5^k+1)))
%Y Cf. A000032, A144837, A371650.
%Y Similar constants: A093540, A338304, A338612, A371647.
%K nonn,cons
%O 1,3
%A _Amiram Eldar_, Mar 31 2024
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