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 A130250 Minimal index k of a Jacobsthal number such that A001045(k)>=n (the 'upper' Jacobsthal inverse). 7

%I

%S 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,

%T 7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%U 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9

%N Minimal index k of a Jacobsthal number such that A001045(k)>=n (the 'upper' Jacobsthal inverse).

%C 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 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 a(10)=5 because A001045(5)=11>=10, but A001045(4)=5<10

%Y For partial sums see A130252. Other related sequences A130249, A130253, A105348. A001045, A130234, A130242.

%K nonn

%O 0,3

%A _Hieronymus Fischer_, May 20 2007

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