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A089959
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a(n)=floor(1/(f(n)-f(n)^2)) with f(n)=frac(n*(sqrt(5)-1)/2) (fractional part).
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3
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4, 5, 8, 4, 12, 4, 4, 19, 4, 6, 6, 4, 30, 4, 5, 10, 4, 9, 5, 4, 48, 4, 5, 7, 4, 15, 4, 4, 14, 4, 7, 5, 4, 77, 4, 5, 8, 4, 10, 4, 4, 24, 4, 6, 6, 4, 22, 4, 4, 11, 4, 8, 5, 4, 124, 4, 5, 7, 4, 13, 4, 4, 16, 4, 7, 6, 4, 39, 4, 5, 9, 4, 9, 5, 4, 35, 4, 6, 6, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Denote by Fn and Ln the Fibonacci resp. Lucas numbers. Then some of the terms follow one of the following two patterns: (1) a(Fn) = (Ln + 1). Example: a(8) = 19 since 8 = F6 and 18 = L6. (2) a(Ln) = (Fn + 1). Example: a(29) = 14 = (F7 + 1) = (13 + 1).
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FORMULA
| a(n) = floor( 1/({n*k}*(1 - {n*k})); k = phi^(-1).
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EXAMPLE
| a(7) = 4 = floor( 1/(.3262379...)*(.67376207...); where {x} = fractional part of x = (7)*(.6180339...)= .3262379...; (1 - {x}) = .67376207...; .6180339... = (sqrt(5)-1)/2 = phi^(-1)
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MATHEMATICA
| Table[Floor[1/(FractionalPart[(2*n)/(1+Sqrt[5])]*(1-FractionalPart[ (2*n)/(1 + Sqrt[5])]))], {n, 1, 80}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jul 01 2007
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PROG
| (PARI) default(realprecision, 200); p=(sqrt(5)-1)/2; vector(100, n, 1\(frac(n*p)-frac(n*p)^2)) \\ M. F. Hasler, Apr 06 2009
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CROSSREFS
| Sequence in context: A143717 A155921 A016721 * A085996 A020804 A021222
Adjacent sequences: A089956 A089957 A089958 * A089960 A089961 A089962
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 16 2003
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EXTENSIONS
| Corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jul 01 2007
Definition, comment and example reworded and corrected by M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 06 2009
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