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%I A371647 #6 Mar 31 2024 08:43:49
%S A371647 1,2,0,0,0,1,3,3,2,8,8,9,0,3,6,9,8,7,6,7,0,7,7,6,4,0,9,5,4,6,8,3,5,5,
%T A371647 0,5,6,4,3,0,5,5,5,0,6,8,8,1,3,8,0,2,6,5,7,3,0,3,6,6,1,3,7,9,4,6,9,2,
%U A371647 6,5,6,7,8,8,5,6,9,4,8,2,4,6,2,8,6,7,7,2,7,9,4,3,4,7,6,7,4,1,0,9,0,7,0,6,2
%N A371647 Decimal expansion of Sum_{k>=0} 1/Fibonacci(5^k).
%C A371647 This constant is a transcendental number (Nyblom, 2001).
%H A371647 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 A371647 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A371647 Equals Sum_{k>=0} 1/A145232(k).
%e A371647 1.20001332889036987670776409546835505643055506881380...
%t A371647 RealDigits[Sum[1/Fibonacci[5^k], {k, 0, 10}], 10, 120][[1]]
%o A371647 (PARI) suminf(k = 0, 1/fibonacci(5^k))
%Y A371647 Cf. A000045, A145232, A371648.
%Y A371647 Similar constants: A079585, A079586, A153386, A153387, A371649.
%K A371647 nonn,cons
%O A371647 1,2
%A A371647 _Amiram Eldar_, Mar 31 2024

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