A234368 Floor(AGM(1, Fibonacci(n))), where AGM denotes the arithmetic-geometric mean.

1, 1, 1, 1, 2, 3, 5, 7, 10, 16, 23, 35, 53, 80, 122, 187, 286, 439, 675, 1041, 1608, 2491, 3864, 6004, 9344, 14563, 22729, 35517, 55566, 87026, 136440, 214117, 336322, 528725, 831868, 1309817, 2063861, 3254227, 5134497, 8106188, 12805344, 20239959

Offset

1,5

Links

Table of n, a(n) for n=1..42.

Formula

a(n) ~ Pi * phi^n / (2 * sqrt(5) * log(phi) * n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio, log(phi) = A002390. - Vaclav Kotesovec, May 09 2016

Example

a(9) = floor(AGM(1, Fibonacci(9))) = floor(AGM(1, 34)) = 10.

Mathematica

Table[Floor[ArithmeticGeometricMean[1, Fibonacci[n]]], {n, 1, 50}] (* Vaclav Kotesovec, May 09 2016 *)

Crossrefs

Cf. A000040, A127758.

Sequence in context: A134792 A300795 A033068 * A052011 A278706 A005468

Adjacent sequences: A234365 A234366 A234367 * A234369 A234370 A234371

Keyword

nonn

Author

Alex Ratushnyak, Dec 25 2013

Status

approved