A288424 Partial sums of A288384.

0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1

Offset: 0

Author

Omar E. Pol, Jun 09 2017

Keywords

• nonn

Comments

It appears that the number of zeros is infinite.

Observation: for at least the first 110 terms the largest distance between two zeros that are between nonzero terms is 3.

Question: are there distances > 3?

From Hartmut F. W. Hoft, Jun 13 2017: (Start)

Yes: a(346..351) = (0,1,2,3,4,0).

Conjecture: a(n) >= 0 for all n >= 0, and a(n) is unbounded.

First occurrences: 3 = a(337) occurring 27 times; 4 = a(350) occurring 8 times; 5 = a(830) occurring 5 times; all through n=2500. (End)

Crossrefs

Cf. A274650, A286294, A288384.

Programs

Mathematica

(* function a288384[] is defined in A288384 *)
a288424[n_] := Accumulate[a288384[n]]
a288424[104] (* data *) (* Hartmut F. W. Hoft, Jun 13 2017 *)

Extensions

Signs reversed at the suggestion of Hartmut F. W. Hoft by Omar E. Pol, Jun 13 2017