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A293419 a(n) is the least integer k such that k/Fibonacci(n) > sqrt(2). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

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

a(n) = A293418(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(ceil(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018

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

CROSSREFS

Cf. A000045, A293418, A293420.

Sequence in context: A152948 A018136 A243853 * A277218 A293643 A022863

Adjacent sequences:  A293416 A293417 A293418 * A293420 A293421 A293422

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 12 2017

STATUS

approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)