A357053 Decimal expansion of Sum_{k>=1} k/Fibonacci(2*k).
2, 3, 9, 7, 4, 1, 4, 1, 8, 7, 9, 1, 6, 5, 2, 1, 2, 0, 0, 4, 0, 9, 2, 2, 4, 4, 9, 5, 6, 8, 1, 7, 7, 8, 7, 0, 8, 5, 2, 0, 7, 2, 2, 2, 9, 6, 3, 7, 5, 5, 4, 4, 4, 8, 5, 8, 3, 1, 9, 7, 3, 7, 0, 8, 7, 2, 8, 2, 3, 7, 7, 7, 8, 9, 3, 2, 2, 1, 5, 9, 9, 2, 3, 2, 8, 7, 6, 1, 8, 6, 8, 5, 6, 7, 0, 3, 3, 6, 6, 5, 1, 0, 8, 4, 9
Offset: 1
Examples
2.39741418791652120040922449568177870852072229637554...
References
- Daniel Duverney, Keiji Nishioka, Kumiko Nishioka, and Iekata Shiokawa, Transcendence of Jacobi's theta series and related results, in: K. Györy, et al. (eds.), Number Theory, Diophantine, Computational and Algebraic Aspects, Proceedings of the International Conference held in Eger, Hungary, July 29-August 2, 1996, de Gruyter, 1998, pp. 157-168.
Links
- Daniel Duverney and Iekata Shiokawa, On series involving Fibonacci and Lucas numbers I, AIP Conference Proceedings, Vol. 976, No. 1. American Institute of Physics, 2008, pp. 62-76.
- Derek Jennings, On reciprocals of Fibonacci and Lucas numbers, Fibonacci Quarterly, Vol. 32, No. 1 (1994), pp. 18-21.
- Eric Weisstein's World of Mathematics, Jacobi Theta Functions.
- Index entries for transcendental numbers.
Crossrefs
Programs
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Mathematica
RealDigits[Sum[k/Fibonacci[2*k], {k, 1, 300}], 10, 100][[1]] -
PARI
sumpos(k=1, k/fibonacci(2*k)) \\ Michel Marcus, Sep 10 2022
Comments