A156351 a(n) = Sum_{k=1..n} (-1)^K(k+1)*(K(k+1)-K(k)) where K(k) = A000002(k).

1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 41, 41, 42, 43, 43, 44, 44, 45, 46, 46, 47, 48, 49, 49

Offset: 1

Author

Benoit Cloitre, Feb 08 2009

Keywords

• nonn

Comments

a(n)=1 plus the number of symbol changes in the first n terms of A078880. - Jean-Marc Fedou and Gabriele Fici, Mar 18 2010

Links

• Jon Maiga, Table of n, a(n) for n = 1..10000
• J.M. Fedou and G. Fici, Some remarks on differentiable sequences and recursivity, Journal of Integer Sequences 13(3): Article 10.3.2 (2010). [From Jean-Marc Fedou and _Gabriele Fici_, Mar 18 2010]

Crossrefs

Partial sums of A156728.

Programs

Mathematica

a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1 + Mod[n - 1, 2]}], {n, 3, 80}, {i, 1, a2[[n]]}]; a[n_] := Sum[(-1)^a2[[k + 1]]*(a2[[k + 1]] - a2[[k]]), {k, 1, n}]; Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Jun 18 2013 *)

Formula

n - A054353(a(n)) = 1 if n is in A078649, n - A054353(a(n)) = 0 otherwise. A078649(n + 1 - a(n)) - n takes values among {0,1,2,3}.

a(n) = gcd(a(a(n-1)),2) + a(n-2) (conjectured). - Jon Maiga, Dec 07 2021