I am so sorry, there appears to have been an alphabetical malfunction, in that I did not say you were a hippopotamus. I said, the hippocampus is the place for short-term memories while the cortex is home to long-term memories and the results, published in the journal Science, showed that memories were formed simultaneously in the hippocampus and the cortex.
I hope that explains why I support Scotland becoming Canada’s 11th province.
Come on, I’m serious, after all Scotland is closer to Newfoundland than Hawaii is to California… and don’t forget, more than half of Canada's prime ministers have claimed Scottish heritage.
“This is timely. I recently extended the sequence of the number of achievable times with N fuses: https://oeis.org/A283075 (scroll down to the bottom). a(13) took 12.5 hours to compute and used 249GB on a machine with 256GB.”
Holey moley! That was timely indeed and as for-
“a(13) took 12.5 hours to compute and used 249GB on a machine with 256GB.”
That is absolutely amazing, I am flabbergasted by your perspicacity, perspicuity and decipherability. I welcome the time when you will be inducted into the A2K Hall of Fame and presented with the Golden Keys to the executive bathroom.
I would however wish to point out that from the example shown in your link:
“…when the first rope's flames have reached the middle…
But as each rope burns at a nonconstant rate, the ‘middle’ is no indicator of time. Or am I missing something? Just sayin’.
Eke beautifully wrote, “This reminds me of the time I was at tending a bar in Wisconsin and three bi-valves mussel up and come in to suck it and see...”
Man, I was just across the street in the Harley-Davidson museum – dagnabbit if that don’t beat all and the answer is plain to sea: https://www.poetryfoundation.org/poems-and-poets/poems/detail/43914
The greatest common divisor (gcd) of two or more integers is the greatest integer that evenly divides those integers. For example, the gcd of 8 and 12 is 4 (usually written as gcd(8,12)=4). Two integers are called coprime (or “relatively prime”) if their gcd is equal to 1.
So a reasonable question to ask is…
Given two randomly chosen integers a and b, what is the probability that gcd(a,b)=1?
If no prime divides n, then n=1, by the fundamental theorem of arithmetic. So we want to find the probability that no prime divides gcd(a,b). Let a and b be two randomly chosen integers and p a fixed prime. If p divides both a and b then gcd(a,b)≥p.
We are interested in the probability that this does not occur for any p.
Now I need to say what I mean by “randomly chosen”. It’s very handwavey, but we will calculate the probability for an integer chosen uniformly at random between 1 and N, and then let N tend to infinity. We won’t actually do that, but that’s what we’re thinking of.
Every pth integer is divisible by p, so the probability that p divides a and b is 1p2, and the probability that it divides at most one of a or b is 1−1p2. That’s a good start, but what we want is this probability over all primes. The probabilities for each prime are independent of each other, so you can just multiply them all together. Therefore the probability that gcd(a,b)=1 is Pr(gcd(a,b)=1)=∏p prime(1−1p2).
Make mine a Harvey Wallbanger ;0)
In this thread, there are 100 members. Each of whom is either crazy or sane.
However, if you choose any two members at random, at least one is crazy.
How many sane members are there?