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A115338
a(n) = Fibonacci(floor(sqrt(n))).
1
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
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
KEYWORD
nonn,easy
AUTHOR
Giuseppe Coppoletta, Mar 06 2006
EXTENSIONS
More terms from Stefan Steinerberger and Jonathan Vos Post, Mar 08 2006
STATUS
approved