This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A141260 #25 Mar 08 2024 11:57:35
%S A141260 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,
%T A141260 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,
%U A141260 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
%N A141260 a(n) = 1 if n == {0,1,3,4,5,7,9,11} mod 12, otherwise a(n) = 0.
%C A141260 Also characteristic function of A141259.
%C A141260 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.
%C A141260 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___...
%C A141260 If we fill the holes with S we get A141260:
%C 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,
%C A141260 ........1.........0.........1.........1.........0.......1.........1.........0...
%C A141260 - the result is
%C A141260 1..0..1.1.1..0..1.0.1..0..1.1.1..0..1.1.1..0..1.0.1.... = A141260
%C A141260 But instead, if we define T recursively by filling the holes in S with the terms of T itself, we get A035263:
%C 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,
%C A141260 ........1.........0.........1.........1.........1.......0.........1.........0...
%C A141260 - the result is
%C A141260 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
%H A141260 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%e A141260 a(16) = 1 since 16 == 4 (mod 12).
%t A141260 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 *)
%Y A141260 Cf. A141259. Note that A035263 has a similar definition, but is a different sequence.
%K A141260 nonn
%O A141260 1,1
%A A141260 _Gary W. Adamson_, Jun 18 2008
%E A141260 Edited by _N. J. A. Sloane_, Jun 28 2008, Jan 14 2009