bio  website  go.helmsnet.de 

location  Germany  
age  61  
visits  member for  3 years, 9 months 
seen  24 mins ago  
stats  profile views  1,056 
Mathematics is only a hobby  although I have done undergrad courses in the 70ties. But part of my job was doing statistics and this kept me near my favourite subject "linear algebra" (programmed factoranalysis and a matrixorientated calculator MatMate). Around 2002 I came in contact with the internetcommunity in mathnewsgroups and could improve my Collatzdiscussion. Next subject was the Bernoullinumbers, then integer matrices and since 2006 the problem of iterated exponentiation aka tetration. Serving halfterm jobs in teaching here at the university I found time to fiddle with that subjects in depth  and found love with the exploratory approach and impulse of the 18'th century numbertheory, namely L.Euler, "the master of us all"...
Due to lack of formal education I've to do my "research" widely on my own  but that's what I just like: to find structure, pattern, laws from the ground.
5h

accepted  Is that seriestransformation known in the context of divergent summation? 
5h

answered  Is that seriestransformation known in the context of divergent summation? 
13h

awarded  Revival 
18h

revised 
How this expression leads to the given sequence
improved explanation, added improved picture 
18h

revised 
How this expression leads to the given sequence
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19h

revised 
How this expression leads to the given sequence
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1d

answered  procedurebased (as opposed to definitionbased) concepts 
Apr 1 
comment 
Can you overcome the 6th degree obstruction?
One could try to make things less insulting simply be the (still extremely impolite and illiterate) <???>son and <???>son (possibly with a plea for excuse not knowing better) to indicate that "Something" is not meant as a jovial/colonialistic gameofname. (Just a proposal) 
Apr 1 
comment 
Is there a known solution to $f(x) = (1x)f(x^2)$?
:) Yes, I'm so used to the ps to pdfconversion by ghostscript in the background that I even forget to mention it... 
Apr 1 
answered  Is there a known solution to $f(x) = (1x)f(x^2)$? 
Mar 16 
revised 
Is that seriestransformation known in the context of divergent summation?
added image whowing the range of summability 
Mar 1 
comment 
Collatz dropping times aperiodicity
(cont) I forgot to mention: the aperiodicity guarantees, that this does not run into a repeated sequence of only one letter but can be continued forever to sharper compressions. If we write the sequence instead as infinite product, beginning with (3/2)*(3/2)*(3/4)*... where we take care that we never fall below 1, then the compression as words provide the "best approximations" of powers of 3 to powers of 2. 
Mar 1 
comment 
Collatz dropping times aperiodicity
even more interesting: there are two types of partial sums, say $a=1,2$ and $b=1,2,2$. Then you can rewrite it $a_1(n)=a,a,a,b,a,a,a,b,a,a,b,a,a,a,b,...$ ,say. THis has again two types of "words",$c=a,a,a,b$ and $d=a,a,b$, say. Then one can rewrite this as $a_2(n) = c,d,d,d,c,d,d,c,d,d,d,....$. Then this has two types of "words"... and so on. It is a nice game to find the ever more compressed expression, and is also related to the continued fraction of log(3)/log(2) (or log(3/2), dan't have it at hand at the moment) 
Feb 16 
revised 
Infinite matrix leading eigenvector problem
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Feb 16 
revised 
Infinite matrix leading eigenvector problem
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Feb 16 
revised 
Infinite matrix leading eigenvector problem
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Feb 16 
revised 
Infinite matrix leading eigenvector problem
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Feb 16 
answered  Infinite matrix leading eigenvector problem 
Feb 16 
comment 
Infinite matrix leading eigenvector problem
I don't know whether you've already observed that the characteristic polynomial factors in terms of qbinomials (with $q=e^{\lambda}$) depending on the size of the matrix? I've seen this for even sizes. (Maybe this gives some hint for the eigenvalues, too.) 
Feb 15 
revised 
Euler's divergent series sum n!*(1)^n: what is known about the resulting constant?
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