This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A273153 #22 May 07 2017 12:07:07
%S A273153 0,1,1,5,3,27,29,121,31,503,507,2037,1021,8179,8185,32753,4095,131055,
%T A273153 131063,524269,262139,2097131,2097141,8388585,2097149,33554407,
%U A273153 33554419,134217701,67108857,536870883,536870897,2147483617,134217727,8589934559,8589934575,34359738333
%N A273153 a(n) = Numerator of (0 followed by 1's) - n/2^n.
%C A273153 A060576(n+1) = 0, 1, 1, 1, 1, 1, 1, ... - (0(n) = Oresme(n) = 0, 1/2, 1/2, 3/8, 1/4, 5/32, 3/32, ...). Both sequences are autosequences of the first kind. f(n) = 0, 1/2, 1/2, 5/8, 3/4, 27/32, 29/32, 121/128, ... is an autosequence of the first kind. Without one 1/2, f(n) is an increasing sequence.
%C A273153 The numerators (1 followed by A075101(n)) are the same as in n/2^n.
%H A273153 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%e A273153 Array of differences of fractions (characteristic aspect of an autosequence of the first kind):
%e A273153 0, 1/2, 1/2, 5/8, 3/4, ...
%e A273153 1/2, 0, 1/8, 1/8, 3/32, ...
%e A273153 -1/2, 1/8, 0, -1/32, -1/32, ...
%e A273153 5/8, -1/8, -1/32, 0, 1/128, ...
%e A273153 -3/4, 3/32, 1/32, 1/128, 0, ...
%e A273153 ...
%t A273153 {0}~Join~Array[Numerator@ Abs[1 - Binomial[0, # - 1] - #/2^#] &, 30] (* _Michael De Vlieger_, May 17 2016 *)
%Y A273153 Cf. A060576, A054977, A075101, A209308.
%K A273153 nonn,frac
%O A273153 0,4
%A A273153 _Paul Curtz_, May 16 2016