bio  website  go.helmsnet.de 

location  Germany  
age  62  
visits  member for  4 years, 8 months 
seen  1 hour ago  
stats  profile views  1,272 
Mathematics is only a hobby  although I have done undergrad courses in the 70s. 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 internet community in math newsgroups and could improve my Collatz discussion. Next subject was the Bernoulli numbers, then integer matrices and since 2006 the problem of iterated exponentiation aka tetration. Serving halftime 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.
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comment 
On an example of an eventually oscillating function
I've found heuristically more properties of $d(x)$, detailed that aspects and gave some hypothetical explanations but still cannot provide proofs. So my followupquestion (and possible answeres) might be interesting. Please see here mathoverflow.net/questions/201098 
2d

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Oscillation aspects of twoway infinite alternating series (a followup from the MOquestion “functions that eventually oscillate”)
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2d

revised 
Oscillation aspects of twoway infinite alternating series (a followup from the MOquestion “functions that eventually oscillate”)
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Mar 26 
asked  Oscillation aspects of twoway infinite alternating series (a followup from the MOquestion “functions that eventually oscillate”) 
Mar 16 
revised 
3n+1 problem and cycles
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Mar 16 
revised 
3n+1 problem and cycles
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Mar 16 
answered  3n+1 problem and cycles 
Mar 15 
comment 
3n+1 problem and cycles
The "cycle" and the "divergence"problem are likely unrelated. In the $5x+1$problem we have cycles, and likely most trajectories diverge. In the $3x+1$problem where we did not yet find any indication of a divergent trajectory, we have nontrivial cycles in the negative numbers. 
Mar 15 
answered  Collatz property implying infinite “fall below” trajectories, is it known? 
Mar 10 
revised 
On an example of an eventually oscillating function
rewrote the whole answer, deleted overcomplicated derivations 
Mar 4 
revised 
On an example of an eventually oscillating function
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Mar 3 
revised 
On an example of an eventually oscillating function
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revised 
On an example of an eventually oscillating function
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revised 
On an example of an eventually oscillating function
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revised 
On an example of an eventually oscillating function
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Mar 2 
revised 
On an example of an eventually oscillating function
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Mar 2 
answered  On an example of an eventually oscillating function 
Feb 28 
comment 
On an example of an eventually oscillating function
Hmm,I just tried to get some advantage from a reformulation for $x$ near $1$, so using $x=1t$ and then to centralize (+ smooth) the oscillation of the result around $1/2$ by writing $g(t)=((1t)1)  ((1t)^21)+((1t)^41)  ... + ... $ and $f(x)=g(1x)+1/2 $), then expand the binomial expressions (by the powers of $(1t)$ and collect like powers of $t$. This gives at each power of $t$ an infinite divergent series but which is alternating and can be normalized by decomposition into geometric series. This gives vanishing coefficients at the $g(t)$series. But I've not yet arrived anywhere... 
Feb 21 
revised 
A question on Collatz's conjecture
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Feb 21 
answered  A question on Collatz's conjecture 