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A140443
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Difference between n-th Fibonacci number and floored n-th power of Viswanath's constant.
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0
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0, 0, 1, 2, 4, 6, 11, 19, 31, 52, 86, 140, 228, 372, 604, 980, 1589, 2575, 4171, 6754, 10933, 17696, 28640, 46349, 75003, 121368, 196390, 317779, 514193, 831999, 1346223, 2178257, 3524519, 5702820, 9227389, 14930266, 24157719, 39088058
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Using the value of Viswanath's constant given by Eric Weisstein's notebook (v = 1.1321506910656020459) makes this sequence different from a(32) forwards; the gap gradually widens after that.
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LINKS
| Eric Weisstein, Random Fibonacci sequence at MathWorld
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FORMULA
| a(n) = F(n) - floor(v^n), where F(n) is given by A000045 with F(1) = F(2) = 1 and v = 1.1319882487943 as given by A078416.
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EXAMPLE
| a(7) = 11 because F(7) = 13 and v^7 is approximately 2.38173, which floored is 2, so 13 - 2 = 11.
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MATHEMATICA
| V = 1.1319882487943; Table[Fibonacci[n] - Floor[V^n], {n, 50}]
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CROSSREFS
| Cf. the Fibonacci numbers A000045, decimal expansion of Viswanath's constant A078416.
Sequence in context: A007053 A005684 A018167 * A115992 A115993 A136424
Adjacent sequences: A140440 A140441 A140442 * A140444 A140445 A140446
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KEYWORD
| nonn
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AUTHOR
| Alonso Delarte (alonso.delarte(AT)gmail.com), Jun 25 2008
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