http://www.maa.org/devlin/LockhartsLament.pdf

It would be nice if we could drill down into an argument to the level of our curiosity. So if you want to know the exact zero you could click to see how to find it with the right equations, but if you’re willing to accept a “good enough for the purpose” approximation then you could just keep reading.

Some day they’ll finish A Young Lady’s Illustrated Primer

http://en.wikipedia.org/wiki/The_Diamond_Age

Clarification:
Using Wolfram Alpha, you can find that the derivative of (36+27*log10(x))-x is 27/(x ln(10))-1, and this function stays at the negative part forever beyond a certain point. Therefore (36+27*log10(x))-x never goes up again.

“All short code samples presented in articles, unless otherwise marked, do not require attribution to when used in your own software. However, I will point out that it’s often very nice (for maintenance reasons) to link to the source of such information in a comment.”

DigitSum(value^3)
<= 9 * DigitCount(value^3)
<=9*(log(value^3) + 1)
<=9*(3*log(value) + 1)
<=27*log(value) + 9

http://www.wolframalpha.com/input/?i=%289+%2B+27+*+log_10%28x%29%29+-+x+from+1+to+100

In terms of your proof, this bound doesn’t matter much, but it starts to be important if, like me, you’re looking at the equivalent of Dudeney numbers with powers much higher than 3.

~Zomega

Anyway, nice demonstration !

Here is just another implementation for interleave-block :

interleave-block: func [block [block!] item /local pos] [
loop subtract length? block 1 [
block: insert next block item
]
return head block
]

if block length is 1 or 0, then no loop occurs, so no item is inserted.

It was interesting for me to try this. I didn’t study proofs of this kind in school (at least not that I remember :P). But I’ve read enough Wikipedia math articles on map coloring and distribution of primes to now grok the strategy of attack. Reading up on hard problems might not get you measurably closer to solving other unsolved problems, but it makes little puzzles like this look trivial by comparison!

I fixed up the code a little…but if anyone has ideas to improve it (that don’t involve taking out parentheses) let me know!