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A140443 Difference between n-th Fibonacci number and floored n-th power of Viswanath's constant. 0
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; text; internal format)
OFFSET

1,4

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.

LINKS

Table of n, a(n) for n=1..38.

Eric Weisstein, Random Fibonacci sequence at MathWorld

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.

EXAMPLE

a(7) = 11 because F(7) = 13 and v^7 is approximately 2.38173, which floored is 2, so 13 - 2 = 11.

MATHEMATICA

V = 1.1319882487943; Table[Fibonacci[n] - Floor[V^n], {n, 50}]

CROSSREFS

Cf. the Fibonacci numbers A000045, decimal expansion of Viswanath's constant A078416.

Sequence in context: A260697 A018167 A295831 * A224957 A115992 A115993

Adjacent sequences:  A140440 A140441 A140442 * A140444 A140445 A140446

KEYWORD

nonn

AUTHOR

Alonso del Arte, Jun 25 2008

STATUS

approved

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Last modified May 13 07:08 EDT 2021. Contains 343836 sequences. (Running on oeis4.)