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Search: id:A115338
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| A115338 |
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a(n)=F([sqrt(n)]), where [k]=integer part of k and F(n) is the Fibonacci sequence. |
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+0
1
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| 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; listen)
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OFFSET
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0,10
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REFERENCES
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D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 62, 1986.
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FORMULA
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Since F(n) = nint((phi^n)/(sqrt(5))) where nint is the nearest integer function and phi is (1 + sqrt 5 )/2 = A001622 we have a(n) = nint((phi^[sqrt(n)])/(sqrt(5))). - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 08 2006
a(n) = F([sqrt(n)]). a(n) = A000045(A000196(n)). a(n) = nint((phi^[sqrt(n)])/(sqrt(5))).
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EXAMPLE
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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.
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MATHEMATICA
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Table[Fibonacci[Floor[Sqrt[n]]], {n, 0, 70}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com)
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CROSSREFS
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Equals A000045(A000196(n)).
Cf. A000045, A000196, A001622.
Sequence in context: A055980 A076080 A134914 this_sequence A133877 A132270 A054896
Adjacent sequences: A115335 A115336 A115337 this_sequence A115339 A115340 A115341
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KEYWORD
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easy,nonn
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AUTHOR
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Giuseppe Coppoletta (gcoverest-11(AT)yahoo.fr), Mar 06 2006
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 08 2006
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