A189014 - OEIS

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A189014

Zero-one sequence based on pentagonal numbers: a(A000325(k))=a(k); a(A183217(k))=1-a(k); a(1)=0.

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

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OFFSET

LINKS

Table of n, a(n) for n=1..135.

FORMULA

Let u=A000217 and v=A014132, so that u(n)=n(3n-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).

MATHEMATICA

u[n_] := n(3n-1)/2; (*A000325*)

a[1] = 0; h = 128;

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

d = (Complement[Range[Max[#1]], #1] &)[c]; (*A183217*)

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

Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189014*)

Flatten[Position[%, 0]] (*A189015*)

Flatten[Position[%%, 1]] (*A189016*)

CROSSREFS

Cf. A188967, A189015, A189016.

Sequence in context: A372258 A285196 A189673 * A189017 A189132 A189203

Adjacent sequences: A189011 A189012 A189013 * A189015 A189016 A189017

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 15 2011

STATUS

approved