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Search: id:A138371
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| A138371 |
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Positions of digits after decimal point of tribonacii constant A058265 (root of polynomial x^3-x^2-x-1) where the approximation to this number by rational fraction does not improve the accuracy. |
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+0
4
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| 4, 5, 6, 7, 9, 12, 15, 17, 19, 21, 24, 25, 27, 28, 34, 38, 39, 41, 49, 50, 51, 56, 58, 64, 68, 69, 71, 72, 76, 77, 81, 85, 86, 88, 91, 95, 98, 100, 102, 104, 105, 107, 109, 111, 112, 113, 115, 117, 124, 126, 129, 133, 135, 136, 139, 142, 145, 148, 149, 151, 153, 160
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Some numbers are giving empty set in this procedure. These numbers are e.g. Golden Ratio=(1+Sqrt[5])/2, Sqrt[2] what mean that if you need improove accuracy one decimal digit we have to uses new fraction with bigger integers as numerator and denominator. For all numbers sequence is that same also for 1/number.
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EXAMPLE
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a(1)=4 because 103/56 approximate Tribonacii constant to 3 and also 4 digits
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MATHEMATICA
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<< NumberTheory`Recognize` b = {}; a = {}; Do[k = Recognize[N[Root[ -1 - #1 - #1^2 + #1^3 &, 1], n + 1], 1, x]; If[MemberQ[a, k], AppendTo[b, n], AppendTo[a, k]], {n, 1, 500}]; b (*Artur Jasinski*)
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CROSSREFS
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Cf. A138335, A138336, A138337, A138338, A138339, A138343, A138366, A138367, A138369, A138370.
Adjacent sequences: A138368 A138369 A138370 this_sequence A138372 A138373 A138374
Sequence in context: A010399 A008523 A047568 this_sequence A139453 A010391 A010419
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KEYWORD
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base,nonn,uned,probation
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Mar 17 2008
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