A105393 Decimal expansion of sum of reciprocals of squares of Fibonacci numbers.
2, 4, 2, 6, 3, 2, 0, 7, 5, 1, 1, 6, 7, 2, 4, 1, 1, 8, 7, 7, 4, 1, 5, 6, 9, 4, 1, 2, 9, 2, 6, 6, 2, 0, 3, 7, 4, 3, 2, 0, 2, 5, 9, 7, 7, 4, 5, 1, 3, 8, 3, 0, 9, 0, 5, 1, 1, 0, 1, 0, 2, 8, 3, 4, 5, 4, 6, 6, 1, 1, 9, 3, 7, 5, 1, 1, 1, 9, 7, 8, 6, 3, 6, 8, 7, 7, 5, 3, 8, 9, 8, 1, 5, 2, 1, 5, 3, 6, 3, 6, 3, 7, 9, 2, 1
Offset: 1
Examples
2.426320751167241187741569...
Links
- Richard André-Jeannin, Irrationalité de la somme des inverses de certaines suites récurrentes, C. R. Acad. Sci. Paris Ser. I Math., Vol. 308, No. 19 (1989), pp. 539-541.
- Daniel Duverney, Keiji Nishioka, Kumiko Nishioka and Iekata Shiokawa, Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 73, No. 7 (1997), pp. 140-142.
- Michel Waldschmidt, Elliptic functions and transcendence, in: Krishnaswami Alladi (ed.), Surveys in number theory, Springer, New York, NY, 2008, pp. 143-188, alternative link. See Corollary 51.
- Eric Weisstein's World of Mathematics, Fibonacci Number.
- Eric Weisstein's World of Mathematics, Lucas Number.
- Eric Weisstein's World of Mathematics, Reciprocal Fibonacci Constant.
- Index entries for transcendental numbers
Programs
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Mathematica
RealDigits[Total[1/Fibonacci[Range[500]]^2],10,120][[1]] (* Harvey P. Dale, May 31 2016 *)
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PARI
sum(k=1,500,1./fibonacci(k)^2) \\ Benoit Cloitre, Jan 07 2006
Formula
Equals Sum_{k>=1} 1/F(k)^2 = 2.4263207511672411877... - Benoit Cloitre, Jan 07 2006
Extensions
More terms from Benoit Cloitre, Jan 07 2006
Comments