A270804 0 followed by the positions of the 1's in the inverse Thue-Morse sequence A270803.

0, 1, 2, 7, 8, 9, 10, 31, 32, 33, 34, 39, 40, 41, 42, 127, 128, 129, 130, 135, 136, 137, 138, 159, 160, 161, 162, 167, 168, 169, 170, 511, 512, 513, 514, 519, 520, 521, 522, 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

Offset

0,3

Links

Table of n, a(n) for n=0..63.

Maciej Gawron, and Maciej Ulas, On formal inverse of the Prouhet-Thue-Morse sequence, Discrete Mathematics 339.5 (2016): 1459-1470. Also arXiv preprintarXiv:1601.04840 [math.CO], 2016.

Formula

See Maple code.

Maple

a:=proc(n) option remember;
if n<=2 then n
elif n=3 then 7
else if n mod 4 = 0 then a(n-1)+1
     elif n mod 4 = 1 then a(n-2)+2
     elif n mod 4 = 2 then a(n-3)+3
     elif n mod 8 = 3 then a(n-3)+7
     else 4*a((n-1)/2)+3; fi;
fi;
end;
[seq(a(n), n=0..120)];

Mathematica

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]];
Table[a[n], {n, 0, 63}] (* Jean-François Alcover, Dec 03 2017, from Maple *)

Crossrefs

Cf. A010060, A270803.

Sequence in context: A283565 A047527 A064517 * A167457 A287515 A260581

Adjacent sequences: A270801 A270802 A270803 * A270805 A270806 A270807

Keyword

nonn

Author

N. J. A. Sloane, Apr 02 2016

Extensions

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).

Status

approved