A293418 -id:A293418 - 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.

A293420 a(n) is the integer k that minimizes |k/Fibonacci(n) - sqrt(2)|.

Original entry on oeis.org

0, 1, 1, 3, 4, 7, 11, 18, 30, 48, 78, 126, 204, 330, 533, 863, 1396, 2258, 3654, 5913, 9567, 15480, 25047, 40527, 65574, 106101, 171676, 277777, 449453, 727230, 1176682, 1903912, 3080594, 4984506, 8065100, 13049606, 21114706, 34164312, 55279019, 89443331

Offset: 0

Clark Kimberling, Oct 12 2017

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

Cf. A000045, A293418, A293419.

[Round(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(round(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018

a(n) = floor(1/2 + Fibonacci(n)*sqrt(2)).

a(n) = A293418(n) if (fractional part of Fibonacci(n)*sqrt(2)) < 1/2, otherwise a(n) = A293419(n).

cp's OEIS Frontend

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

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