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A189011 Zero-one sequence based on triangular numbers: a(A000217(k))=a(k); a(A014132(k))=1-a(k); a(1)=0. 4

%I #7 Mar 30 2012 18:57:23

%S 0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,

%T 0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,1,

%U 0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,1

%N Zero-one sequence based on triangular numbers: a(A000217(k))=a(k); a(A014132(k))=1-a(k); a(1)=0.

%e Let u=A000217 and v=A014132, so that u(n)=n(n+1)/2 and v=complement(u) for n>=1. Then a is a self-generating zero-one sequence with initial value a(1)=0 and a(u(k))=a(k); a(v(k))=1-a(k).

%t u[n_] := n(n+1)/2; (*A000217*)

%t a[1] = 0; h = 128;

%t c = (u[#1] &) /@ Range[h];

%t d = (Complement[Range[Max[#1]], #1] &)[c]; (*A014132*)

%t Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];

%t Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189011*)

%t Flatten[Position[%, 0]] (*A189012*)

%t Flatten[Position[%%, 1]] (*A189013*)

%Y Cf. A188967, A189012, A189013, A188973.

%K nonn

%O 1

%A _Clark Kimberling_, Apr 15 2011

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Last modified April 19 10:56 EDT 2024. Contains 371791 sequences. (Running on oeis4.)