Search: id:A089959
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%I A089959
%S A089959 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,
%T A089959 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,
%U A089959 4,7,6,4,39,4,5,9,4,9,5,4,35,4,6,6,4
%N A089959 a(n)=floor(1/(f(n)-f(n)^2)) with f(n)=frac(n*(sqrt(5)-1)/2) (fractional 
               part).
%C A089959 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).
%F A089959 a(n) = floor( 1/({n*k}*(1 - {n*k})); k = phi^(-1).
%e A089959 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)
%t A089959 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
%o A089959 (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
%Y A089959 Sequence in context: A143717 A155921 A016721 this_sequence A085996 A020804 
               A021222
%Y A089959 Adjacent sequences: A089956 A089957 A089958 this_sequence A089960 A089961 
               A089962
%K A089959 nonn
%O A089959 1,1
%A A089959 Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 16 2003
%E A089959 Corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Jul 01 2007
%E A089959 Definition, comment and example reworded and corrected by M. F. Hasler 
               (MHasler(AT)univ-ag.fr), Apr 06 2009

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