A130250 - OEIS

%I #14 Mar 19 2023 03:34:44

%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).

%H G. C. Greubel, <a href="/A130250/b130250.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = ceiling(log_2(3n-1)) = 1 + floor(log_2(3n-2)) for n >= 1.

%F a(n) = A130249(n-1) + 1 = A130253(n-1) for n >= 1.

%F G.f.: (x/(1-x))*Sum_{k>=0} x^A001045(k).

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

%t Table[If[n==0, 0, Ceiling[Log[2, 3*n-1]]], {n,0,120}] (* _G. C. Greubel_, Mar 18 2023 *)

%o (Magma) [0] cat [Ceiling(Log(2,3*n-1)): n in [1..120]]; // _G. C. Greubel_, Mar 18 2023

%o (SageMath)

%o def A130250(n): return 0 if (n==0) else ceil(log(3*n-1, 2))

%o [A130250(n) for n in range(121)] # _G. C. Greubel_, Mar 18 2023

%Y For partial sums see A130252.

%Y Cf. A001045, A105348, A130234, A130242, A130249, A130253.

%K nonn

%O 0,3

%A _Hieronymus Fischer_, May 20 2007