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 A140443 Difference between n-th Fibonacci number and floored n-th power of Viswanath's constant. 0

%I #4 Oct 12 2012 14:38:24

%S 0,0,1,2,4,6,11,19,31,52,86,140,228,372,604,980,1589,2575,4171,6754,

%T 10933,17696,28640,46349,75003,121368,196390,317779,514193,831999,

%U 1346223,2178257,3524519,5702820,9227389,14930266,24157719,39088058

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

%C 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.

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/RandomFibonacciSequence.html">Random Fibonacci sequence</a> at MathWorld

%F 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.

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

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

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

%K nonn

%O 1,4

%A _Alonso del Arte_, Jun 25 2008

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Last modified February 29 14:25 EST 2024. Contains 370425 sequences. (Running on oeis4.)