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A293418
a(n) is the greatest integer k such that k/Fibonacci(n) < sqrt(2).
3
0, 1, 1, 2, 4, 7, 11, 18, 29, 48, 77, 125, 203, 329, 533, 862, 1395, 2258, 3654, 5912, 9567, 15479, 25047, 40527, 65574, 106101, 171675, 277776, 449452, 727229, 1176682, 1903911, 3080594, 4984506, 8065100, 13049606, 21114706, 34164312, 55279018, 89443331
OFFSET
0,4
LINKS
FORMULA
a(n) = floor(Fibonacci(n)*sqrt(2)).
a(n) = A293419(n) - 1 for n > 0.
MATHEMATICA
z = 120; r = Sqrt[2]; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}]; (* A293418 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293419 *)
Table[Round[r*f[n]], {n, 0, z}]; (* A293420 *)
PROG
(PARI) for(n=0, 30, print1(floor(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018
(Magma) [Floor(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // G. C. Greubel, Feb 08 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 12 2017
STATUS
approved