1,1

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

Period 12: 1,0,1,1,1,0,1,0,1,0,1,1. [From Paolo P. Lava (ppl(AT)spl.at), Feb 11 2009]

Index entries for characteristic functions

a(n)=(1/396)*{4*[(n-1) mod 12]+4*(n mod 12)-29*[(n+1) mod 12]+37*[(n+2) mod 12]-29*[(n+3) mod 12]+37*[(n+4) mod 12]-29*[(n+5) mod 12]+37*[(n+6) mod 12]+4*[(n+7) mod 12]+4*[(n+8) mod 12]-29*[(n+9) mod 12]+37*[(n+10) mod 12]}, with n>=1 [From Paolo P. Lava (ppl(AT)spl.at), Feb 11 2009]

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

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

Sequence in context: A120530 A078616 A104106 this_sequence A029883 A035263 A089045

Adjacent sequences: A141257 A141258 A141259 this_sequence A141261 A141262 A141263

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 18 2008

Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 28 2008, Jan 14 2009