A115338 - OEIS

%I #19 Sep 26 2023 15:11:14

%S 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,

%T 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,

%U 13,13,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,34,34,34,34,34

%N a(n) = Fibonacci(floor(sqrt(n))).

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

%H John M. Campbell, <a href="/A115338/a115338.pdf">Sums of Fibonacci Numbers Indexed by Integer Parts</a>, Fibonacci Q., 61 (2023), 143-152.

%F 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

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

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

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

%e a(143) = F([sqrt(143)]) = F([11.958]) = F(11) = 89,

%e a(144) = F([sqrt(144)]) = F([12]) = F(12) = 144,

%e a(145) = F([sqrt(145)]) = F([12.042]) = F(12) = 144.

%t Table[Fibonacci[Floor[Sqrt[n]]], {n, 0, 70}] (* _Stefan Steinerberger_, Mar 08 2006 *)

%Y Cf. A000045, A000196, A001622.

%K nonn,easy

%O 0,10

%A _Giuseppe Coppoletta_, Mar 06 2006

%E More terms from _Stefan Steinerberger_ and _Jonathan Vos Post_, Mar 08 2006