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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 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 17:16 EDT 2020. Contains 334630 sequences. (Running on oeis4.)