#math overflow

[trivalentlinks]

so you all know i'm one of those people who's very much in support of leaving comments on old fics if you liked them, because the author probably still wants to know if someone is loving their old fic

(i've probably reblogged some tumblr posts to this effect)

but i was just browsing stack overflow and saw the comments on one of the answers, and the first (oldest) one said something to the effect of "it's been 8 years, but this is still great :)" and others were all just praising the answer, remarking on how helpful it still was even so many years later; another comment, from 10 years later just said "brilliant. perfect."

and it occurred to me that for all the times that i've reblogged posts about commenting years later, or posts that said something to the effect of, "if you don't have the time or energy to give a more in depth comment, just saying 'loved it' is enough to make an author's day",

i have literally never commented on a stack overflow answer (unless i had a technical comment, ie the kind of comment that would probably be called 'con-crit' over in fandom and frowned upon), even when it made my life immeasurably better

... and i probably still won't, since people so rarely do and i would feel awkward and weird being the only one making a non-technical comment, but there have been so many times when i've wanted to, and gosh i wish letting someone know when they improved your day were part of the culture, there, too

(i do get why stack overflow's culture would want to prioritize actually technically relevant comments, because if you're just looking for a discussion so you can all arrive at the correct answer, that's probably more important than letting the author know how much you loved their answer and how helpful you found it,

but gosh, there have been times when i'd been struggling with something for ages and someone wrote exactly what i needed and i just wanted to virtually kiss them for it. maybe there should be a separate thank-the-author comment section)

[obis]

A129935 - Numbers n such that ceiling( 2/(2^{1/n}-1) ) is not equal to floor( 2n/(log 2) )

A129935 - Numbers n such that ceiling( 2/(2^{1/n}-1) ) is not equal to floor( 2n/(log 2) )

777451915729368, 140894092055857794, 1526223088619171207, ...

Something a little different today. The other day on Reddit's Math subsite, there was a thread about statements that appeared true for all n less than something large. The first example given was Skewes' Number, a number where it's been proven that the number of primes is finally greater than the logarithmic integral. The definition isn't important, but if you had tested the first hundred quintillion integers (which would take a while) you might have convinced yourself that π(n) < li(n) forever. But it's not. Since 1933, Skewes' number has shrunk from the original eee79 -- it is now somewhere around 10316.

One comment links to a question on Math Overflow with a similar premise. That thread links to several interesting integer sequences in addition to the above. For instance, A102567 are counterexamples to "There is no positive integer n such that the concatenation of n with itself is a square" -- the first is 13223140496.

But the golden egg in those two threads must be a paper called The Strong Law Of Small Numbers by Richard K. Guy. Read through that paper, and try to decide which of them are actually true and which of them have a counter example at some large n.