A115338 a(n) = Fibonacci(floor(sqrt(n))).

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34

Offset

0,10

References

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 62, 1986.

Links

Table of n, a(n) for n=0..85.

John M. Campbell, Sums of Fibonacci Numbers Indexed by Integer Parts, Fibonacci Q., 61 (2023), 143-152.

Formula

Since F(n) = round((phi^n)/(sqrt(5))), where phi is (1 + sqrt 5 )/2 = A001622, we have a(n) = round((phi^[sqrt(n)])/(sqrt(5))). - Jonathan Vos Post, Mar 08 2006

a(n) = F([sqrt(n)]).

a(n) = A000045(A000196(n)).

a(n) = round((phi^[sqrt(n)])/(sqrt(5))).

Example

a(143) = F([sqrt(143)]) = F([11.958]) = F(11) = 89,
a(144) = F([sqrt(144)]) = F([12]) = F(12) = 144,
a(145) = F([sqrt(145)]) = F([12.042]) = F(12) = 144.

Mathematica

Table[Fibonacci[Floor[Sqrt[n]]], {n, 0, 70}] (* Stefan Steinerberger, Mar 08 2006 *)

Crossrefs

Cf. A000045, A000196, A001622.

Sequence in context: A257639 A180447 A295866 * A348522 A226046 A133877

Adjacent sequences: A115335 A115336 A115337 * A115339 A115340 A115341

Keyword

nonn,easy

Author

Giuseppe Coppoletta, Mar 06 2006

Extensions

More terms from Stefan Steinerberger and Jonathan Vos Post, Mar 08 2006

Status

approved