A255738 a(1) = 1; for n > 1, a(n) = 1*0^{A000120(n-1) - 1}.

1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1

Comments

Also the characteristic function of A094373.

Essentially the same as A036987 and A209229, except for the indexing.

Also the second row of square array A255740.

The definition related to binary weight (A000120) arises from the general formula of the square array A255740.

Partial sums give A070941, the second row of the square array A255741.

After the initial 1,1,1, we see runs of 2^m-1 0's (m=1,2,3,...) followed by a single 1. - N. J. A. Sloane, Mar 16 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata with even rule numbers, 2016. See Eq. (72).

Index entries for characteristic functions

Mathematica

A255738[n_] := Boole[BitAnd[n-1, n-2] == 0]; Array[A255738, 100] (* or *)
Join[{1}, Differences[BitLength[Range[100] - 1]]] (* Paolo Xausa, Feb 18 2026 *)

Prog

(PARI) a(n) = if (n==1, 1, 0^(hammingweight(n-1)-1));

Crossrefs

Cf. A000007, A000120, A011782, A036987, A040000, A070941, A094373, A151787, A145682, A209229, A255740, A255741.

Sequence in context: A116915 A266178 A339653 * A296209 A076141 A011751

Adjacent sequences: A255735 A255736 A255737 * A255739 A255740 A255741

Keyword

nonn,less

Author

Michel Marcus and Omar E. Pol, Mar 16 2015

Status

approved