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Search: id:A085422
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| A085422 |
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A sequence analogous to the Lucas numbers (A000032), with ratios converging to Pi. |
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+0
3
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| -1, 2, 4, 13, 40, 125, 392, 1231, 3867, 12148, 38164, 119895, 376661, 1183315, 3717493, 11678848, 36690183, 115265609, 362117590, 1137625960, 3573957358, 11227918180, 35273545269, 110815110683, 348135937628, 1093701304102
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The Lucas numbers have 1 = phi - 1/phi where this sequence has k, and the ratios of the Lucas numbers converge to phi.
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FORMULA
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a(0) = -1, a(1) = 2, a(n+2) = floor[k*a(n+1)+a(n)], where k = Pi - 1/Pi = 2.82328276....
Lim(n->inf) a(n)/a(n-1) = Pi.
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EXAMPLE
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a(5) = floor[(Pi - 1/Pi)*40+13] = 125.
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CROSSREFS
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Cf. A000032.
Adjacent sequences: A085419 A085420 A085421 this_sequence A085423 A085424 A085425
Sequence in context: A093630 A033091 A133453 this_sequence A065601 A118930 A087214
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KEYWORD
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sign,easy
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 29 2003
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EXTENSIONS
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Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), Feb 1 2005
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