A156728 a(n) = abs(A054354(n)).

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

Offset: 1

Author

Benoit Cloitre, Feb 14 2009

Keywords

• nonn

Comments

This sequence is the image of the Kolakoski sequence A000002 under the morphism 1->1, 2->01. - Gabriele Fici, Aug 12 2013

Links

• Jean-Marc Fedou and Gabriele Fici, Some remarks on differentiable sequences and recursivity, Journal of Integer Sequences 13(3): Article 10.3.2 (2010).

Crossrefs

Cf. A000002, A054354, A156251, A156253.

Programs

Mathematica

a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1 + Mod[n - 1, 2]}], {n, 3, 105}, {i, 1, a2[[n]]}]; a[n_] := Mod[a2[[n]] + a2[[n + 1]], 2]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Jun 18 2013 *)

Formula

a(n) = (v(n+1) - v(n) + 1)/2 where v(n) = A156253(n) - A156251(n).

a(n) = (A000002(n) + A000002(n+1)) mod 2.

a(n) = A156253(n+1) - A156253(n). - Alan Michael Gómez Calderón, Dec 20 2024