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a(n) = log_2((1+A002426(n))/numerator((1+A002426(n))/2^n)).
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%I #7 Feb 28 2017 22:35:19

%S 0,1,2,3,2,2,1,1,2,2,1,1,1,1,2,3,2,2,1,1,1,1,3,2,1,1,3,2,2,2,1,1,2,2,

%T 1,1,1,1,3,2,1,1,2,4,3,3,1,1,1,1,3,2,3,3,1,1,2,2,1,1,1,1,2,3,2,2,1,1,

%U 1,1,3

%N a(n) = log_2((1+A002426(n))/numerator((1+A002426(n))/2^n)).

%H G. C. Greubel, <a href="/A186037/b186037.txt">Table of n, a(n) for n = 0..1000</a>

%t b[n_] := If[n < 0, 0, 3^n Hypergeometric2F1[1/2, -n, 1, 4/3]];

%t a[n_] := Log[2, (1 + b[n])/Numerator[(1 + b[n])/2^n]]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Feb 27 2017 *)

%K nonn,easy

%O 0,3

%A _Paul Barry_, Feb 11 2011