Search: id:A130234
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%I A130234
%S A130234 0,1,3,4,5,5,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,
%T A130234 10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,
%U A130234 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11
%N A130234 Minimal index k of a Fibonacci number such that Fib(k)>=n (the 'upper' 
               Fibonacci Inverse).
%C A130234 Inverse of the Fibonacci sequence (A000045), nearly, since a(Fib(n))=n 
               except for n=2 (see A130233 for another version). a(n+1) is equal 
               to the partial sum of the Fibonacci indicator sequence (see A104162).
%F A130234 a(n)=ceiling(log_phi((sqr(5)*n+sqr(5*n^2-4))/2))=ceiling(arcosh(sqr(5)*n/
               2)/ln(phi)) where phi=(1+sqr(5))/2. Also true: a(n)=A130233(n-1)+1 
               for n>0. G.f.: g(x)=x/(1-x)*sum{k>=0, x^Fib(k)}.
%F A130234 a(n)=ceiling(log_phi(sqr(5)*n-1)) for n>=1, where phi is = the golden 
               ratio. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 
               2007
%e A130234 a(10)=7, since Fib(7)=13>=10 but Fib(6)=8<10.
%Y A130234 Partial sums: A130236. Other related sequences: A000045, A130234, A130256, 
               A130260, A104162, A108852, A130256, A130260, Lucas Inverse: A130241 
               - A130248.
%Y A130234 Sequence in context: A120677 A098200 A092405 this_sequence A108852 A119476 
               A037038
%Y A130234 Adjacent sequences: A130231 A130232 A130233 this_sequence A130235 A130236 
               A130237
%K A130234 nonn
%O A130234 0,3
%A A130234 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007

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