[seqfan] Near-linear sequence

[Charles Greathouse]

Sequence A101402 appears to be nearly linear. For the first 10,000 terms
there is a constant k such that |a(n) - kn| < 2 (e.g., take k = 0.355). Can
anyone prove or disprove that a(n) = kn + O(1) for some constant k? In the
(likely?) latter case, can another reasonable bound be found, maybe O(log
n)? I can't even think of a technique that would work here.

I just checked to a million and it looks like the same holds. Here I used k
= 0.3549419505. Probably going to 10 million would require relaxing the
bound slightly; already by a million the choice of constant is very
constrained.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University