Constant C=0.1688... for A081881 seems to be wrong
Rainer Rosenthal
r.rosenthal at web.de
Thu Jan 24 23:45:18 CET 2008
David W. Cantrell wrote:
> You seem to have forgotten what I wrote on Jan. 9 in your sci.math
> thread "Inverse Harmonic Series". I not only confirmed the few digits
> that BC had given for the constant, but I also gave many more.
> Furthermore, I gave a conjectured formula for the sequence.
You are right and I am sorry for the mistakes I made.
In this post I want to ask one more question about BC's constant
and I also want to tell about a strange response from Superseeker.
> Of course, since we can now calculate more elements of the sequence
> very easily, we can also specify C with much greater accuracy. Indeed,
> it seems that we can even give a formula for the sequence
>
> a(n) = 1 + floor(C*exp(n)) (*)
>
> where
>
> C = 0.1688563566671442037316797755009010341...
I tried in vain to understand how you arrived at (*). I could have asked
in sci.math but I think it appropriate to ask here instead of hopping
elsewhere.
Now my Superseeker problem:
With the corrected formula I played to find more and more decimals of
this interesting constant C. In the course of playing I made up a new sequence and
encountered a strange reply from Superseeker:
=========================================================================================
Report on [ 21,43,65,86,108,130,152,173,195,217,238,260,282,304,325,347,369,390,412,434,
456,477,499,521,542,564,586,608,629,651,673,694,716,738,760,781,803,825,847]:
Many tests are carried out, but only potentially useful information
(if any) is reported here.
SUGGESTION: apparently the differences of order 1 in the
difference table of depth 1 have become constant.
If this is true then the next four terms of the sequence are:
[869, 891, 913, 935]
TEST: ARE DIFFERENCES OF SOME LEVEL PERIODIC?
SUGGESTION: Differences of order 1
appear to be periodic. If so next 2 terms are:
825 846
==========================================================================================
While the SUGGESTION makes sense I am upset about the "next two terms".
(BTW The correct continuation is 868, 890, 912, 933, 955.)
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