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A141260 a(n) = 1 if n == {0,1,3,4,5,7,9,11} mod 12, otherwise a(n) = 0. 3
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 (list; graph; refs; listen; history; text; internal format)
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

Period 12: 1,0,1,1,1,0,1,0,1,0,1,1. [From Paolo P. Lava, Feb 11 2009]

LINKS

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

Index entries for characteristic functions

FORMULA

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, Feb 11 2009]

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: A078616 A257477 A104106 * 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

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Last modified November 16 04:54 EST 2018. Contains 317257 sequences. (Running on oeis4.)