A270804 - OEIS

%I #13 Dec 03 2017 02:09:35

%S 0,1,2,7,8,9,10,31,32,33,34,39,40,41,42,127,128,129,130,135,136,137,

%T 138,159,160,161,162,167,168,169,170,511,512,513,514,519,520,521,522,

%U 543,544,545,546,551,552,553,554,639,640,641,642,647,648,649,650,671,672,673,674,679,680,681,682,2047

%N 0 followed by the positions of the 1's in the inverse Thue-Morse sequence A270803.

%H Maciej Gawron, and Maciej Ulas, <a href="http://dx.doi.org/10.1016/j.disc.2015.12.016">On formal inverse of the Prouhet-Thue-Morse sequence</a>, Discrete Mathematics 339.5 (2016): 1459-1470. Also <a href="http://arxiv.org/abs/1601.04840">arXiv preprint</a>arXiv:1601.04840 [math.CO], 2016.

%F See Maple code.

%p a:=proc(n) option remember;

%p if n<=2 then n

%p elif n=3 then 7

%p else if n mod 4 = 0 then a(n-1)+1

%p      elif n mod 4 = 1 then a(n-2)+2

%p      elif n mod 4 = 2 then a(n-3)+3

%p      elif n mod 8 = 3 then a(n-3)+7

%p      else 4*a((n-1)/2)+3; fi;

%p fi;

%p end;

%p [seq(a(n),n=0..120)];

%t a[n_] := a[n] = Which[n <= 2, n, n == 3, 7, True, Which[Mod[n, 4] == 0, a[n - 1] + 1, Mod[n, 4] == 1, a[n - 2] + 2, Mod[n, 4] == 2, a[n - 3] + 3, Mod[n, 8] == 3, a[n - 3] + 7, True, 4*a[(n - 1)/2] + 3]];

%t Table[a[n], {n, 0, 63}] (* _Jean-François Alcover_, Dec 03 2017, from Maple *)

%Y Cf. A010060, A270803.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 02 2016

%E Perhaps someone could enter the sequences d_n, z_n, u_n given in Section 4 of the article (unless of course they are already in the OEIS).