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Search: id:A105394
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| A105394 |
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Decimal expansion of sum of reciprocals of squares of Lucas numbers. |
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+0
2
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| 1, 2, 0, 7, 2, 9, 1, 9, 9, 6, 9, 8, 5, 7, 4, 7, 0, 7, 4, 4, 1, 7, 2, 0, 4, 1, 8, 4, 2, 5, 7, 6, 9, 9, 9, 4, 5, 3, 0, 6, 9, 2, 1, 4, 5, 4, 0, 1, 9, 0, 3, 6, 3, 7, 6, 9, 5, 1, 3, 1, 1, 5, 9, 4, 2, 2, 1, 2, 2, 4, 0, 0, 1, 5, 4, 0, 7, 0, 3, 5, 7, 7, 6, 1, 6, 7, 7, 6, 5, 5, 9, 7, 8, 6, 8, 8, 9, 9, 9, 2
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is one of a set of related number theory constants. It is conjectured to be irrational. T. D. Noe (noe(AT)sspectra.com) extended the digits of this constant to 100 digits accuracy, when J. V. Post had discovered it and found it to 8 digits. The reciprocal Fibonacci constant sum 1/F(n) ~ 3.35988566 is given in A079586, queried as to irrationality by Erdos and proved irrational by Andre-Jeannin (1989). The reciprocal Lucas constant sum 1/L(n) ~ 1.96285817 is given in A093540. Sum 1/L(n)^2 converges because each term is equal or less than the corresponding term in the converging reciprocal Lucas constant. The sum 1/F(n)^2 is given in A105393.
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REFERENCES
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R. Andre-Jeannin, "Irrationalite de la somme des inverses de certaines suites recurrentes." C. R. Acad. Sci. Paris Ser. I Math. 308, 539-541, 1989.
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LINKS
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Eric Weisstein's World of Mathematics, Lucas Number.
Eric Weisstein's World of Mathematics, Fibonacci Number.
Eric Weisstein's World of Mathematics, Reciprocal Fibonacci Constant.
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FORMULA
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Decimal expansion of Sum 1/L(n)^2.
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EXAMPLE
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1.207291996985747074417204
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CROSSREFS
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Cf. A079586, A093540, A105393.
Sequence in context: A022897 A156442 A140663 this_sequence A011343 A021486 A104540
Adjacent sequences: A105391 A105392 A105393 this_sequence A105395 A105396 A105397
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 04 2005
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