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%I #18 Sep 08 2022 08:45:30
%S 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 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,
%U 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 Number of Jacobsthal numbers (A001045) <=n.
%C Partial sums of the Jacobsthal indicator sequence (A105348).
%C For n<>1, we have a(A001045(n))=n+1.
%H G. C. Greubel, <a href="/A130253/b130253.txt">Table of n, a(n) for n = 0..10000</a>
%H Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, <a href="https://doi.org/10.2478/auom-2021-0002">On some new results for the generalised Lucas sequences</a>, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 17-36.
%F a(n) = floor(log_2(3n+1)) + 1 = ceiling(log_2(3n+2)).
%F a(n) = A130249(n) + 1 = A130250(n+1).
%F G.f.: 1/(1-x)*(Sum_{k>=0} x^A001045(k)).
%e a(9)=5 because there are 5 Jacobsthal numbers <=9 (0,1,1,3 and 5).
%t Table[1+Floor[Log[2,3n+1]],{n,0,100}] (* _Harvey P. Dale_, Jul 03 2013 *)
%o (PARI) a(n)=logint(3*n+1,2)+1 \\ _Charles R Greathouse IV_, Oct 03 2016
%o (Magma) [Ceiling(Log(3*n+2)/Log(2)): n in [0..30]]; // _G. C. Greubel_, Jan 08 2018
%Y For partial sums see A130252. Other related sequences A001045, A130249, A130250, A130253, A105348. Also A130233, A130235, A130241, A108852, A130245.
%K nonn,easy
%O 0,2
%A _Hieronymus Fischer_, May 20 2007
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