13,153 reputation
11759
bio website go.helms-net.de
location Kassel, Germany
age 62
visits member for 4 years, 3 months
seen 3 hours ago

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 factor-analysis and a matrix-orientated 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 half-time 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.


1d
comment Does this sequence have any mathematical significance?
Just an idea, not an answer: I think to have a better relation to usual mathematical expressions and make the problem more "algebraic", one could mirror the initial sequence and then prepend instead of append. You initial word "001" is then "100" and the binary interpretation is $a_0=4$. Then pre pending the leading subsequence "10" means adding $(2^1) \cdot (2 \cdot 4)$ to $a_0$ to get $a_1=20$. Then iterate. This might be easier to handle, and possibly results in some Collatz-like iteration
1d
answered Old oxford scholarship question: $a^ab^b \ge a^bb^a$
2d
awarded  Good Answer
Dec
12
awarded  Nice Question
Dec
11
comment Application of Mergesort
@MaryStar: yes, that's what I've also thought (but did not actually consider thoroughly). Thanks for the clarification.
Dec
10
comment Application of Mergesort
??? But, if you have found that you need N games = N hours, isn't that simply N/4 hours, if you have four stadiums? And for more stadiums: the same, except that the same person cannot play in the same hour at different places, so to have, say, 100 stadiums does not help much. But you probably cannot mean such a simple question?
Dec
10
comment Application of Mergesort
Hmm, perhaps I've difficulties to understand now, what "stadiums" mean here? I didn't have the idea that the number of stadiums would change the number of competitions, only the possibility to make a clever arrangement to allow two or more games at a time. So if you assume that the number of stadiums might influence the number of comparisions/games, you must have something else in your mind, haven't you?
Dec
10
answered Application of Mergesort
Dec
8
awarded  Caucus
Dec
8
comment Zeta and Gamma function regularization with $\omega=1/0$
I've exercised much with similar questions and think that there is something more general in this. An early discussion of a not too remotely far might be seen here: go.helms-net.de/math/divers/ProblemWithBellmatrix.pdf . Here I stumbled on a curious discrepancy when summing zetas and which could be explained if one introduces $1/\omega$ into the power series for the $\exp(x)$-function.
Dec
8
comment Zeta and Gamma function regularization with $\omega=1/0$
Didi you notice, that the coefficients at the $\gamma$ and the constant follow the first and second column in the matrix of Stirling numbers 1st kind? (Just adapt the factorial coefficients). Then the set of the constants (with adapted factorials) has $\log(1+x)^2$ as its generating function, and the set of coefficients at the $\gamma$ that of the $\log(1+x)$... The same with the $\omega$: so the sum over all that results for the $\omega$s has then somehow $\log(1+\omega)$ involved (don't know about the significance of this at the moment...)
Dec
7
comment Alternate proofs for Collatz 1-Cycles
Fred, maybe I misunderstand something here. You know, I've proved that by this method for N about 10^25000 by doing it explicitely using the convergents of the continued fractions of log(3)/log(2) (this allows to do it only for critical values determined by that convergents) . But I failed to find an argument for the general statement: "for all" ... Do you have a different thing in mind here?
Dec
7
comment Alternate proofs for Collatz 1-Cycles
I've never seen a proof of the inequality, and after all my failing attempts so far (and that of others) I know it must be very difficult... It is directly relatedto /convertible into the open detail in Waring's problem. Can you show how you would prove this?
Dec
5
comment The nonexistence of the Collatz-“1-cycle” by an elementary proof - am I missing something?
[late comment]:Today I just adapted the [tag], no developing of the question was made/intended and I think there is nothing new to say about that Q
Dec
5
revised The nonexistence of the Collatz-“1-cycle” by an elementary proof - am I missing something?
tags extended
Dec
5
comment What do these contour maps tell me about my Collatz expression?
No , a 1-cycle would be the set of the following numbers $a_1,a_2,a_3,...,a_n$ where $a_{k+1}=(3 a_k+1)/2$ and $a_1 = (3a_n+1)/2^A$ with some positive integer A. The only such set in the positive odd numbers is $(a_k)=(1)$ (proven by R. Steiner 1977) but over the negative integers we have $(a_k)=(-1)$ and $(a_1,a_2)=(-5,-7)$. (The set beginning with $-17$ forms a 2-cycle with elements $(-17,-25,-37,-55, -41,-61,-91)$)
Dec
5
comment What do these contour maps tell me about my Collatz expression?
Perhaps relevant: math.stackexchange.com/questions/108489/…
Dec
5
revised The nonexistence of the Collatz-“1-cycle” by an elementary proof - am I missing something?
added 26 characters in body
Dec
4
comment What do these contour maps tell me about my Collatz expression?
Once you have ${ 2\over3 }{ 3^r-1\over2^r-2 } $ this is always non-integer because in the denominator you've the primefactor $3$ but not in the numerator...
Nov
25
comment Determine whether the series $\displaystyle\sum_{n=0}^\infty\frac{2^{n^2}}{n!}$ is convergent or divergent.
Please can we delete this (now?) meaningless answer?