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A115338 a(n)=F([sqrt(n)]), where [k]=integer part of k and F(n) is the Fibonacci sequence. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

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

Equals A000045(A000196(n)).

Cf. A000045, A000196, A001622.

Sequence in context: A257639 A180447 A295866 * A226046 A133877 A132270

Adjacent sequences:  A115335 A115336 A115337 * A115339 A115340 A115341

KEYWORD

easy,nonn

AUTHOR

Giuseppe Coppoletta, Mar 06 2006

EXTENSIONS

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

STATUS

approved

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Last modified May 26 16:47 EDT 2019. Contains 323597 sequences. (Running on oeis4.)