[seqfan] Re: Near-linear sequence

[Frank Adams-Watters]

Perhaps we could get a definition for A101433 while we're at it.

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>

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