This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338304 #13 Jan 05 2025 19:51:41
%S A338304 1,4,9,7,9,2,0,3,8,0,9,9,9,0,6,2,7,1,9,8,7,0,6,8,5,5,5,3,9,9,2,8,5,9,
%T A338304 6,0,8,0,7,2,0,7,7,1,9,8,5,7,0,8,5,9,7,0,4,0,4,9,3,2,2,3,9,8,9,5,4,0,
%U A338304 5,2,7,7,6,9,5,3,2,2,3,7,8,3,9,9,3,2,1
%N A338304 Decimal expansion of Sum_{k>=0} 1/L(2^k), where L(k) is the k-th Lucas number (A000032).
%C A338304 Erdős and Graham (1980) asked whether this constant is irrational or transcendental.
%C A338304 Badea (1987) proved that it is irrational, and André-Jeannin (1991) proved that it is not a quadratic irrational in Q(sqrt(5)), in contrast to the corresponding sum with Fibonacci numbers, Sum_{k>=0} 1/F(2^k) = (7-sqrt(5))/2 (A079585).
%C A338304 Bundschuh and Pethö (1987) proved that it is transcendental.
%H A338304 Richard André-Jeannin, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/29-2/andre-jeannin.pdf">A note on the irrationality of certain Lucas infinite series</a>, The Fibonacci Quarterly, Vol. 29, No. 2 (1991), pp. 132-136.
%H A338304 Catalin Badea, <a href="https://doi.org/10.1017/S0017089500006868">The irrationality of certain infinite series</a>, Glasgow Mathematical Journal, Vol. 29, No. 2 (1987), pp. 221-228.
%H A338304 Peter Bundschuh and Attila Pethö, <a href="https://doi.org/10.1007/BF01547953">Zur transzendenz gewisser Reihen</a>, Monatshefte für Mathematik, Vol. 104, No. 3 (1987), pp. 199-223, <a href="https://eudml.org/doc/178351">alternative link</a>.
%H A338304 Paul Erdős and Ronald L. Graham, <a href="http://www.math.ucsd.edu/~fan/ron/papers/80_11_number_theory.pdf">Old and new problems and results in combinatorial number theory</a>, L'enseignement Mathématique, Université de Genève, 1980, pp. 64-65.
%H A338304 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A338304 Equals 1 + Sum_{k>=0} 1/A001566(k).
%e A338304 1.49792038099906271987068555399285960807207719857085...
%t A338304 RealDigits[Sum[1/LucasL[2^n], {n, 0, 10}], 10, 100][[1]]
%Y A338304 Cf. A000045, A000032, A001566, A079585, A338305.
%K A338304 nonn,cons
%O A338304 1,2
%A A338304 _Amiram Eldar_, Oct 21 2020