A140443 Difference between n-th Fibonacci number and floored n-th power of Viswanath's constant.

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

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