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

0,10

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)

Links

Table of n, a(n) for n=0..104.

Mathematica

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

Crossrefs

Cf. A274650, A286294, A288384.

Sequence in context: A117886 A145723 A085977 * A127325 A368750 A259660

Adjacent sequences: A288421 A288422 A288423 * A288425 A288426 A288427

Keyword

nonn

Author

Omar E. Pol, Jun 09 2017

Extensions

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

Status

approved