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September 18, 2018 8:08 AM Subscribe
Pick a number, any number and this fun little site will show how it is the sum of three palindromes! It doesn't seem like it should be possible, but it always is, in any base, and most of the time there's more than one way to do it.
It doesn't seem like it should be possible
counting single digit numbers as palindromes seems to make this a bit easier to believe
posted by thelonius at 8:23 AM on September 18, 2018 [14 favorites]
counting single digit numbers as palindromes seems to make this a bit easier to believe
posted by thelonius at 8:23 AM on September 18, 2018 [14 favorites]
in any base,
Any base ≥ 5, per the linked paper. 176 (101100002) provides a counterxample in base 2. It remains an open question in bases 3 and 4 although the authors believe it to be true.
posted by DevilsAdvocate at 8:49 AM on September 18, 2018 [6 favorites]
Any base ≥ 5, per the linked paper. 176 (101100002) provides a counterxample in base 2. It remains an open question in bases 3 and 4 although the authors believe it to be true.
posted by DevilsAdvocate at 8:49 AM on September 18, 2018 [6 favorites]
Also featured on a Numberphile episode just yesterday.
posted by Hairy Lobster at 8:56 AM on September 18, 2018 [2 favorites]
posted by Hairy Lobster at 8:56 AM on September 18, 2018 [2 favorites]
Yeah, it doesn't really get interesting until you hit 6+ digits. Seeing how, for example, 8 can be represented as 8 + 0 + 0 is not compelling at all.
posted by grumpybear69 at 9:07 AM on September 18, 2018 [7 favorites]
posted by grumpybear69 at 9:07 AM on September 18, 2018 [7 favorites]
I found the one number in the standard base that won't work, but it's my secret number only I know about.
posted by GoblinHoney at 9:24 AM on September 18, 2018 [1 favorite]
posted by GoblinHoney at 9:24 AM on September 18, 2018 [1 favorite]
Ditto what Thelonius and Grumpy said . While I know "5" might technically be a palindrome, I don't think of it as such, because if I was sitting with friends trying to come up with palindromes, anyone who said "Oh, I've got a good one: 'E'!" would have things thrown at them.
But yes it does get cooler with huge numbers.
posted by senor biggles at 9:36 AM on September 18, 2018 [4 favorites]
But yes it does get cooler with huge numbers.
posted by senor biggles at 9:36 AM on September 18, 2018 [4 favorites]
I should add that it's remarkable that it can be proved for all bases >= 5! Even proving it for base 10 would be amazing
posted by thelonius at 10:19 AM on September 18, 2018
posted by thelonius at 10:19 AM on September 18, 2018
This page reminded me of zombo.com. You can do anything there, including create number palindromes.
posted by tallmiddleagedgeek at 10:19 AM on September 18, 2018 [3 favorites]
posted by tallmiddleagedgeek at 10:19 AM on September 18, 2018 [3 favorites]
Yeah, it doesn't really get interesting until you hit 6+ digits. Seeing how, for example, 8 can be represented as 8 + 0 + 0 is not compelling at all.
Yes, but it can also be represented as 6+1+1 or 4+4+0 or 1+2+5! So fascinating.
posted by jeather at 12:06 PM on September 18, 2018
Yes, but it can also be represented as 6+1+1 or 4+4+0 or 1+2+5! So fascinating.
posted by jeather at 12:06 PM on September 18, 2018
this is super neat!
also if you put in a palindrome it's just that + 0 + 0, which... i guess is right, but so unsatisfying.
posted by numaner at 2:58 PM on September 18, 2018
also if you put in a palindrome it's just that + 0 + 0, which... i guess is right, but so unsatisfying.
posted by numaner at 2:58 PM on September 18, 2018
889 = 888 + 1 + 0
You don't say. Huh.
posted by slogger at 11:00 AM on September 19, 2018 [1 favorite]
You don't say. Huh.
posted by slogger at 11:00 AM on September 19, 2018 [1 favorite]
The proof for bases 2,3 and 4, completing the theorem, was published a year after this one: Sums of Palindromes: an Approach via Automata.
posted by warpy at 6:53 AM on September 21, 2018
posted by warpy at 6:53 AM on September 21, 2018
(And it's trivially true in unary.)
posted by a snickering nuthatch at 7:26 AM on September 21, 2018
posted by a snickering nuthatch at 7:26 AM on September 21, 2018
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posted by jedicus at 8:20 AM on September 18, 2018 [2 favorites]