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A271573 Numerator of (0 followed by A005126(n)= 2, 4, 7, ...)/2^n.

%I A271573 #33 Sep 08 2022 08:46:16
%S A271573 0,1,1,7,3,21,19,71,17,265,261,1035,515,4109,4103,16399,2049,65553,
%T A271573 65545,262163,131077,1048597,1048587,4194327,1048579,16777241,
%U A271573 16777229,67108891,33554439,268435485,268435471,1073741855,67108865,4294967329,4294967313
%N A271573 Numerator of (0 followed by A005126(n)= 2, 4, 7, ...)/2^n.
%C A271573 Reduced fractions: f(n) = 0, 1, 1, 7/8, 3/4, 21/32, 19/32, 71/128, 17/32, 265/512, 261/512, ... .
%C A271573 f(n) is an autosequence of the first kind.
%H A271573 Robert Price, <a href="/A271573/b271573.txt">Table of n, a(n) for n = 0..101</a>
%F A271573 a(n) = numerator(n/2^n + (if n<2 0 else 1)/2), a formula using Oresme numbers n/2^n. - _Jean-François Alcover_, Apr 28 2016 after _Paul Curtz_
%e A271573 a(0), a(1), a(2), a(3), a(4), are the numerators of reduced fractions 0/1, 2/2, 4/4, 7/8, 12/16, ... .
%t A271573 Prepend[Table[Numerator[(2^n + n + 1)/2^(n + 1)], {n, 0, 100}], 0] (* _Robert Price_, Apr 10 2016 *)
%t A271573 (* Computation from Oresme numbers n/2^n: *) a[n_] := Numerator[n/2^n + If[n < 2, 0, 1]/2]; (* _Jean-François Alcover_, Apr 28 2016, after _Paul Curtz_ *)
%o A271573 (PARI) a(n) = if(n==0, 0, numerator((2^(n-1)+n)/2^n)); \\ _Altug Alkan_, Apr 10 2016
%o A271573 (Magma) [0] cat [Numerator((2^(n-1)+n)/2^n): n in [1..40]]; // _Vincenzo Librandi_, Oct 13 2017
%Y A271573 Cf. A000004, A000079, A005126, A006519, A060576(n+1), A075101, A198631, A279635 (denominator).
%K A271573 nonn,frac
%O A271573 0,4
%A A271573 _Paul Curtz_, Apr 10 2016