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A288424
Partial sums of A288384.
3
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)
MATHEMATICA
(* function a288384[] is defined in A288384 *)
a288424[n_] := Accumulate[a288384[n]]
a288424[104] (* data *) (* Hartmut F. W. Hoft, Jun 13 2017 *)
CROSSREFS
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