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

Author

Alonso del Arte, Jun 25 2008

Keywords

• nonn

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.

Examples

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

Links

• Eric Weisstein, Random Fibonacci sequence at MathWorld

Crossrefs

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

Programs

Mathematica

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

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.