378 reputation
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location London, United Kingdom
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visits member for 4 years, 7 months
seen Jan 21 at 9:26

I am a professional programmer, and a recreational mathematician with particular interest in Number Theory.


Sep
24
awarded  Autobiographer
Nov
21
comment Does this algorithm terminate in all scenarios?
Ok, presumably it needs an extra termination check for |A| <= k after step 2 then; from your example, I also infer that d_x^(A,k) is intended to be defined over the k nearest points in A excluding x itself otherwise we have d_x^(A,1) = 0 whenever x is in A.
Nov
21
comment Does this algorithm terminate in all scenarios?
Is the algorithm intended to be asymmetrical, as written? I'd have expected steps (2) and (3) to be reversed, so that the evaluation of A' and B' are acting symmetrically over the full set of n+m vectors.
Oct
28
awarded  Quorum
Jun
25
awarded  Revival
Sep
4
awarded  Critic
May
15
awarded  Yearling
Oct
17
comment Subset higher power sum question (related to quadratic forms)
q.v. = quod vide, Latin for "Google it".
Oct
13
answered A balls-and-colours problem
Oct
10
answered How to characterize a Self-avoiding path.
Oct
4
awarded  Enlightened
Oct
4
awarded  Nice Answer
Sep
18
comment Solve in positive integers $n!=m^2$
m=1, n=0 or 1. For larger n, there is a prime between n/2 and n, which guarantees an unsquared prime factor in the factorial.
Sep
14
answered What's the simplest rational not expressible as a sum of a given number of unit fractions?
Sep
4
comment Does War have infinite expected length?
Moving the played cards to the bottom of the winner's stack in random order makes it much harder to retain a stable cyclic formation, so this result seems not at all surprising, and minimally informative about the answer for any variant without the randomness.
Aug
17
comment Upper bound on number of lines in a linear space given degree bounds
Oops, I misread it, my apologies.
Aug
17
comment Upper bound on number of lines in a linear space given degree bounds
I see nothing in the definition to disallow for any q the case of each line consisting of just 2 points. Then given n points there are $C(n,2)-(n-1)$ lines not containing a given point, and you can always take n large enough to make this exceed $q^2$. What am I missing?
Aug
11
comment On the constants in the Cameron-Erdös conjecture on sum-free subsets.
The OEIS sequence has a link to a table of the first 70 terms, and both Maple and Mathematica code to calculate more values.
Jul
28
comment What's the simplest rational not expressible as a sum of a given number of unit fractions?
I haven't checked the intervening numbers, but by hand I found 289/299 = 1/2 + 1/3 + 1/8 + 1/156 + 1/552. I checked also just using the greedy algorithm, and that gives 1/2 + 1/3 + 1/8 + 1/122 + 1/39795 + 1/1935522680. So I have no idea what Pegg's numbers are supposed to represent, but I can't see any relation between them and the stated problem. Time permitting I'll try calculating the sequence, but I anticipate the correct denominators will grow much more rapidly, so it'll be hard to calculate more than 7-8 terms.
Jul
28
comment What's the simplest rational not expressible as a sum of a given number of unit fractions?
14/17 = 1/2 + 1/4 + 1/14 + 1/476 appears to be an error; I believe 16/17 = 1/2 + 1/3 + 1/10 + 1/128 + 1/32640 is the simplest requiring 5 terms.