A293420 -id:A293420 - cp's OEIS frontend

A293419 a(n) is the least integer k such that k/Fibonacci(n) > sqrt(2).

0, 2, 2, 3, 5, 8, 12, 19, 30, 49, 78, 126, 204, 330, 534, 863, 1396, 2259, 3655, 5913, 9568, 15480, 25048, 40528, 65575, 106102, 171676, 277777, 449453, 727230, 1176683, 1903912, 3080595, 4984507, 8065101, 13049607, 21114707, 34164313, 55279019, 89443332

Offset: 0

Clark Kimberling, Oct 12 2017

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A000045, A293418, A293420.

[Ceiling(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // G. C. Greubel, Feb 08 2018

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 *)

for(n=0, 30, print1(ceil(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018

a(n) = ceiling(Fibonacci(n)*sqrt(2)).

a(n) = A293418(n) + 1 for n > 0.

A293418 a(n) is the greatest integer k such that k/Fibonacci(n) < sqrt(2).

Original entry on oeis.org

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

Clark Kimberling, Oct 12 2017

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A000045, A293419, A293420.

[Floor(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // G. C. Greubel, Feb 08 2018

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 *)

for(n=0,30, print1(floor(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018

a(n) = floor(Fibonacci(n)*sqrt(2)).

a(n) = A293419(n) - 1 for n > 0.

cp's OEIS Frontend

A293419 a(n) is the least integer k such that k/Fibonacci(n) > sqrt(2).

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