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%I #46 Sep 08 2022 08:45:44
%S 1,3,5,7,9,11,13,15,17,19,3,23,25,27,29,31,33,35,37,39,41,43,45,47,49,
%T 51,53,55,57,59,61,9,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,
%U 97,99,101,103,15,107,109,111,113,115,117,119,121,123,125,127
%N Numerator of (2*n+1)/(2^(2*n+1)-1).
%C This first differs from A005408 (the odd numbers 2n+1) at a(10). The sequence of differences is A160145. This explains the similarity of A009843 (expansion of x/cos(x)) and A160143. A156769 describes a similar companion to A036279 (expansion of tan(x)).
%H Altug Alkan, <a href="/A160144/b160144.txt">Table of n, a(n) for n = 0..10000</a>
%p seq(numer((2*n+1)/(4^(2*n+1)-2^(2*n+1))),n=0..32);
%p seq(numer((2*n+1)/(2^(2*n+1)-1)),n=0..50); # _Altug Alkan_, Apr 21 2018
%t Array[Numerator[(2 # + 1)/(2^(2 # + 1) - 1)] &, 64, 0] (* _Michael De Vlieger_, Apr 21 2018 *)
%o (PARI) vector(80,n, n--; numerator((2*n+1)/(4^(2*n+1)-2^(2*n+1)))) \\ _Michel Marcus_, Jan 31 2015
%o (PARI) forstep(k=1, 1e3, 2, print1(numerator(k/(2^k-1)), ", ")); \\ _Altug Alkan_, Apr 21 2018
%o (Magma) [Numerator((2*n+1)/(2^(2*n+1)-1)): n in [0..70]]; // _Vincenzo Librandi_, Apr 25 2018
%Y Cf. A005408, A009843, A036279, A156769, A160143, A160145, A303449 (denominators).
%K easy,frac,nonn
%O 0,2
%A _Peter Luschny_, May 03 2009
%E More terms from _Michel Marcus_, Jan 31 2015
%E Name simplified by _Altug Alkan_, Apr 21 2018
%E Further edited by _N. J. A. Sloane_, Apr 24 2018