Search: id:A130250
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%I A130250
%S A130250 0,1,3,3,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,
%T A130250 7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%U A130250 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
%N A130250 Minimal index k of a Jacobsthal number such that A001045(k)>=n (the 'upper' 
               Jacobsthal inverse).
%C A130250 Inverse of the Jacobsthal sequence (A001045), nearly, since a(A001045(n))=n 
               except for n=2 (see A130249 for another version). a(n+1) is equal 
               to the partial sum of the Jacobsthal indicator sequence (see A105348).
%F A130250 a(n)=ceiling(log_2(3n-1))=1+floor(log_2(3n-2)) for n>=1. Also true: a(n)=A130249(n-1)+1=A130253(n-1) 
               for n>=1. G.f.: g(x)=x/(1-x)*sum{k>=0, x^A001045(k)}.
%e A130250 a(10)=5 because A001045(5)=11>=10, but A001045(4)=5<10
%Y A130250 For partial sums see A130252. Other related sequences A130249, A130253, 
               A105348. A001045, A130234, A130242.
%Y A130250 Sequence in context: A136546 A058729 A021303 this_sequence A130253 A075324 
               A134993
%Y A130250 Adjacent sequences: A130247 A130248 A130249 this_sequence A130251 A130252 
               A130253
%K A130250 nonn
%O A130250 0,3
%A A130250 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 20 2007

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