A141260 a(n) = 1 if n == {0,1,3,4,5,7,9,11} mod 12, otherwise a(n) = 0.

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

Offset

1,1

Comments

Also characteristic function of A141259.

Let S be the period-3 sequence (1,0,1,1,0,1,1,0,1,...); create a hole after every (1,0,1) segment getting 1,0,1__1,0,1__1,0,1__1,0,1,__1,0,1___,... Then insert successive terms of S into the holes.

In more detail: define S to be 1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1,0,1___...

If we fill the holes with S we get A141260:

1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0,

........1.........0.........1.........1.........0.......1.........1.........0...

- the result is

1..0..1.1.1..0..1.0.1..0..1.1.1..0..1.1.1..0..1.0.1.... = A141260

But instead, if we define T recursively by filling the holes in S with the terms of T itself, we get A035263:

1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0, 1___1, 0,

........1.........0.........1.........1.........1.......0.........1.........0...

- the result is

1..0..1.1.1..0..1.0.1..0..1.1.1..0..1.1.1..0..1.1.1.0.1.0.1..0..1.1.1..0..1.0.1.. = A035263

Links

Table of n, a(n) for n=1..108.

Index entries for characteristic functions

Example

a(16) = 1 since 16 == 4 (mod 12).

Mathematica

Table[If[MemberQ[{0, 1, 3, 4, 5, 7, 9, 11}, Mod[n, 12]], 1, 0], {n, 110}] (* or *) PadRight[{}, 110, {1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1}] (* Harvey P. Dale, Mar 29 2015 *)

Crossrefs

Cf. A141259. Note that A035263 has a similar definition, but is a different sequence.

Sequence in context: A323045 A104106 A349167 * A029883 A035263 A089045

Adjacent sequences: A141257 A141258 A141259 * A141261 A141262 A141263

Keyword

nonn

Author

Gary W. Adamson, Jun 18 2008

Extensions

Edited by N. J. A. Sloane, Jun 28 2008, Jan 14 2009

Status

approved