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May
18
awarded  Revival
May
18
awarded  Teacher
May
18
answered What does it mean to have a lone plus sign in the exponent/superscript (Modified Weiszfeld algorithm)
May
9
awarded  Critic
May
9
awarded  Citizen Patrol
Feb
18
comment Characterization of Extended Lucky Numbers
That's because the first few numbers appear in groups of 4, so they create four nearby gaps. The next run is much longer (the numbers from 841 to 3453 - 28 numbers I think) - so the next "staircase" will be much longer than 3 "steps". This means that the gap distribution will follow the same pattern as the numbers themselves.
Feb
18
comment Characterization of Extended Lucky Numbers
Ugh, sorry, didn't save it. I basically used the Mathematica code I posted for the PPCG challenge that inspired this question, and wrapping the body of the For loop in a Do[...,{m}]. (And then I just fed the result for ListPlot and ListLogPlot.)
Feb
18
comment Characterization of Extended Lucky Numbers
Here are the first 500 numbers. Here is a plot of them. And here is a log plot. That last run continues until n = 841 (the next number to be sieved out). Note that each of the gaps corresponds to one of the numbers in the sequence. (The last 4 gaps occur at n in {205, 233, 253, 285}.) And conversely, the long runs correspond to gaps in the sequence.
Feb
11
revised Uniformly Random Tuples
added 146 characters in body
Feb
11
comment Uniformly Random Tuples
@leonbloy Yes, any algorithm could remove those first, but since it didn't make a difference, I figured it would simplify the problem statement to use general multisets (instead of multisets which don't contain more than $n$ copies of any number).
Feb
11
revised Uniformly Random Tuples
added 218 characters in body
Feb
11
comment Uniformly Random Tuples
@AndreiRykhalski Ah yes, that would probably work. I'll add a note about rejection-based algorithms.
Feb
11
awarded  Editor
Feb
11
revised Uniformly Random Tuples
added 152 characters in body
Feb
11
comment Uniformly Random Tuples
No, as the $3$s are indistinguishable, there is only one copy of $(3,3)$ in the pool to draw from (just as there is one copy of $(2,2)$), so they should have the same probability.
Feb
11
awarded  Student
Feb
11
asked Uniformly Random Tuples
Sep
24
awarded  Autobiographer
Jul
18
comment How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once?
I'm pretty sure the sum you figured out for n = 2 is exactly the same as L-choose-2. There could be a smaller number for n > 2, though.
Nov
23
awarded  Supporter