

A140443


Difference between nth Fibonacci number and floored nth 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
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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



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.


KEYWORD

nonn


AUTHOR



STATUS

approved



