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A338304 Decimal expansion of Sum_{k>=0} 1/L(2^k), where L(k) is the k-th Lucas number (A000032). 2
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, 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, 5, 2, 7, 7, 6, 9, 5, 3, 2, 2, 3, 7, 8, 3, 9, 9, 3, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Erdős and Graham (1980) asked whether this constant is irrational or transcendental.

Badea (1987) proved that it is irrational, and Andre-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).

Bundschuh and Pethö (1987) proved that it is transcendental.

LINKS

Table of n, a(n) for n=1..87.

Richard Andre-Jeannin, A note on the irrationality of certain Lucas infinite series, The Fibonacci Quarterly, Vol. 29, No. 2 (1991), pp. 132-136.

Catalin Badea, The irrationality of certain infinite series, Glasgow Mathematical Journal, Vol. 29, No. 2 (1987), pp. 221-228.

Peter Bundschuh and Attila Pethö, Zur transzendenz gewisser Reihen, Monatshefte für Mathematik, Vol. 104, No. 3 (1987), pp. 199-223, alternative link.

Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980, p. 64-65.

FORMULA

Equals 1 + Sum_{k>=0} 1/A001566(k).

EXAMPLE

1.49792038099906271987068555399285960807207719857085...

MATHEMATICA

RealDigits[Sum[1/LucasL[2^n], {n, 0, 10}], 10, 100][[1]]

CROSSREFS

Cf. A000045, A000032, A001566, A079585, A338305.

Sequence in context: A004159 A092554 A155787 * A179222 A123157 A154684

Adjacent sequences:  A338301 A338302 A338303 * A338305 A338306 A338307

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Oct 21 2020

STATUS

approved

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Last modified September 22 07:37 EDT 2021. Contains 347605 sequences. (Running on oeis4.)