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A137203 Number of Fibonacci numbers less than or equal to n^2. 1
1, 3, 5, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

David A. Corneth, Table of n, a(n) for n = 0..9999

Planet Math, list of Fibonacci numbers.

FORMULA

a(n) = A108852(n^2). - Michel Marcus, Aug 03 2014

EXAMPLE

When n=1, the number of Fibonacci numbers less than or equal to 1 is 3.

When n=2, the number of Fibonacci numbers less than or equal to 4 is 5.

When n=3, the number of Fibonacci numbers less than or equal to 9 is 7.

When n=4, the number of Fibonacci numbers less than or equal to 16 is 8.

MATHEMATICA

fibPi[n_] := 1 + Floor[ Log[ GoldenRatio, 1 + n*Sqrt@ 5]]; Array[ fibPi[#^2] &, 80, 0] (* Robert G. Wilson v, Aug 03 2014 *)

PROG

(PARI) first(n) = { res = vector(n+1); fibs = List([0, 1]); i = 2; n2 = n^2; f = 1; while(f <= n2, listput(fibs, f); i++; f = fibonacci(i) ); for(i = 1, #fibs, res[ceil(sqrt(fibs[i]))+1]++ ); for(i = 2, #res, res[i]+=res[i-1]); res} \\ David A. Corneth, Mar 28 2021

CROSSREFS

Cf. A000045, A108852.

Sequence in context: A163301 A036593 A086674 * A102890 A008520 A217129

Adjacent sequences:  A137200 A137201 A137202 * A137204 A137205 A137206

KEYWORD

nonn

AUTHOR

Parthasarathy Nambi, Apr 04 2008

EXTENSIONS

Corrected and extended by Robert G. Wilson v, Aug 03 2014

STATUS

approved

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Last modified October 1 00:53 EDT 2022. Contains 357127 sequences. (Running on oeis4.)