Any positive number can be written as a sum of three palindromes

Post by JadeNB » Tue, Sep 18, 2018, 7:45 PM UTC

tzs wrote: post #34

If a(n) is the number of ways to write n as the sum of three palindromes, the sequence a(0), a(1), a(2), a(3) is kind of interesting. http://oeis.org/A261132

Post by theoh » Tue, Sep 18, 2018, 8:08 PM UTC

brk wrote: post #51

It seems to go for the "least interesting" result. eg: I gave it 363 and it gave me back 363 + 0 + 0, which while technically true, 121 + 121 + 121 would have been more in the spirit of it, IMO. Or even 242 + 121 + 0 would be a little easier than just reusing the original palindrome number with zeros.

Post by dllthomas » Tue, Sep 18, 2018, 8:25 PM UTC

TomMarius wrote: post #105

JadeNB wrote: post #101

Earlier quoted context omitted.

> The real physical universe doesn't offer tooling for playing with advanced math, though. The real physical universe is nothing but tooling for playing with advanced math (but it's not always easy to figure out what the advanced math is, or how best to play with it).

IMHO that's like saying higher level programming languages than assembly are unnecessary. Or that a debugger is useless. And not just the learning purposes. Imagine the possibilities if we could properly simulate (and speed up the simulation) the world - what if we could use genetic algorithms to develop an organism.

Post by tzs » Tue, Sep 18, 2018, 10:21 PM UTC

JadeNB wrote: post #102

tzs wrote: post #34

If a(n) is the number of ways to write n as the sum of three palindromes, the sequence a(0), a(1), a(2), a(3) is kind of interesting. http://oeis.org/A261132

> If a(n) is the number of ways to write n as the sum of three palindromes, the sequence a(0), a(1), a(2), a(3) is kind of interesting. Do you just mean "the sequence a(n)"? I don't see anything especially interesting about the first 4 terms.

Post by industriousthou » Wed, Sep 19, 2018, 5:14 AM UTC

shaded-enmity wrote: post #79

CydeWeys wrote: post #40

For those wondering, this works in every base ≥ 5, according to the original paper: https://arxiv.org/abs/1602.06208v2 Every time I see something like this that is dependent on base-10 representation, I'm always curious to know whether it generalizes, or if it's a quirk specific to base-10 representation. For example, being able to tell if a number is divisible by 2 or 5 by only looking at the last digit.

Yeah, for example to check if a number is divisible by 3, we can use the digit sum and check if the result is divisible by 3, e.g. 153=(1)+(5)+(3)=9. This works in base-10, but we can generalize this by converting the dividend X into (3* X+1)-base then doing a digit sum. Let's say we want to check whether 238 is divisible by 17, so our base is 3* 17+1=52, 238 in base-52 is (4)+(30)=34=2* 17. If the convert-to-arbitra…