A137203 Number of Fibonacci numbers less than or equal to n^2.

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

Offset: 0

Author

Parthasarathy Nambi, Apr 04 2008

Keywords

• nonn

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..9999
• Planet Math, list of Fibonacci numbers.

Crossrefs

Cf. A000045, A108852.

Programs

Mathematica

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

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

Formula

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

Extensions

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