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The most boring integer (up to 300)

If you have been following Every integer is interesting and Part 2, you will see that we have come up with reasons for why the first 300 integers are interesting in their own way. Sometimes, the properties are not great, but we overlook that in the spirit of going further.

We have now taken a breather, so that people can nominate what is the most boring integer. This is how the process will work:

  1. Comment with what you think is the most boring number (that someone has not stated). Include the "interesting property" that was stated.
  2. If you agree with someone else, vote up on their comment.
  3. If you disagree that a number is boring, reply with an interesting factoid about it.

Note by Calvin Lin
2 years, 1 month ago

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298

$2.98 is the most common price at the Dollar Store? Gee, 298 is boring. Have we finally found our candidate? Okay, 298 squared is 88804, the only second number to have the property of its square starting with three identical digits.

Brian Charlesworth · 2 years, 1 month ago

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@Brian Charlesworth It is the only number for which if you search on wikipedia it redirects you to another number(i.e.290) Shobhit Singh · 2 years ago

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@Shobhit Singh Actually, this is the case for many numbers, including all numbers from 291 to 299. Brian Charlesworth · 2 years ago

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@Brian Charlesworth I don't think so bcoz Year 298 (CCXCVIII) was a common year starting on Saturday of the Julian calendar. Shobhit Singh · 2 years ago

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@Brian Charlesworth I agree that, except for the fact you see this number all the time as a price, this is a particularly unremarkable number mathematically. However, in making the final decision which is the most boring, I think looks should matter--i.e., the plainest, most forgettable number should be the winner. So, for example, I think 178 or even 226 looks even more plainer than 298. But that's just a personal opinion. Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin I guess that it's all in the eye of the beholder. I like the look of \(178\) since \(1 + 7 = 8.\) \(226\) is pretty plain, but at least it looks like it did a mirror-check before heading out the door. \(298\) looks like it forgot to shave and decided to wear a checked shirt with a striped tie, (which might actually be hipster fashion, making it that much more distasteful). And as for all the shade being thrown at \(284,\) at least it doesn't look boring, (as you've noted), and its amicability seems to me like a significant feature.

P.S.. If you have a moment, could you check out this question. I have issues with the posted answer and I'd appreciate your input. Thanks. :) Brian Charlesworth · 2 years, 1 month ago

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@Brian Charlesworth We should get the nominees up on stage, so what do we have here so far?

[122], [178], 226, [249], [284], 298

[...] indicates de-nominated numbers, see comments elsewhere.

Now, which one is the hardest to "make interesting" math-properties-wise?

Of the six, only 226 is a "small order figurate number". That basically leaves 298, as the winner of the most boring number. Dollar Store number, how boring is that? It is exactly twice another Dollar Store number, 149.

I have not been able to find any interesting math properties of 298 as of yet

298 BC--"Ptolemy gives his stepdaughterTheoxena in marriage to Agathocles of Syracuse"

What I do notice is, which is kind of what's to be expected, is that the number of hits goes down as the number goes up. That is, the bigger the [random] number, the fewer special properties it has. For example, Wikipedia lists fewer and fewer numbers with four or more digits as having any notable properties at all. So, by that measure, 298 should be the hardest to "make interesting".

Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin I agree with all the de-nominations, and as mentioned elsewhere, \(226\) does have a couple of mildly interesting factoids associated with it. The "Dollar Store Number" doesn't even have that dubious honour going for it up north of the border; prices tend to end in a \(9\) here. Feeling sorry for \(298,\) I gave it another chance but came up empty, just as you did. Unless someone can come up with something soon, I think we may have a winner. Brian Charlesworth · 2 years, 1 month ago

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@Brian Charlesworth There IS a Dollar Store here nearby--it became real popular right after the Wall Street crash in 2008. But I've noticed that business has been dropping off lately, so either 1) the economy is getting better, or 2) people are really going broke. It's right across the street from a coffee shop, so once in a great while, I check prices in there. $2.98 is something I do see a lot--I always think, "I thought this is supposed to be a dollar store?"

Anyway, I propose we vote 298 as the winner of the Most Boring Number Less Than 300, unless someone else can discover some special mathematical talent 298 has. Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin I can't find nice property about \(298\) but I managed to create this: \(298=1 \times 298 = (1+2)^2+(9+8)^2\). Nihar Mahajan · 2 years, 1 month ago

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@Nihar Mahajan Propose an alternative winner, and I'll see if I can find something like that for the alternate.

Here's an excellent approximation for \( \pi\)

\(\left( 2.98 \right) \left( 1+\sqrt { 3 } \right) -5=3.1415...\)

This is how one can make pi out of dog food. Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin I can't find as such. I think this must be extended to 400.Or we can just declare \(298\) as the winner. Nihar Mahajan · 2 years, 1 month ago

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@Michael Mendrin https://www.easycalculation.com/number-properties-of-298.html Shobhit Singh · 2 years ago

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@Shobhit Singh Thank you for pointing out that 298 is an "unhappy, sad, deficient number that is not anything else of any interest"! Michael Mendrin · 2 years ago

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@Michael Mendrin I'll second your proposal. If no objections are raised by 8 a.m. GMT then we can make it official. Brian Charlesworth · 2 years, 1 month ago

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@Brian Charlesworth By midnight here, PST, then. Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin And there we have it; \(298\) is officially the most boring positive integer up to \(300.\)

@Calvin Lin Looks like we're done here. :) Brian Charlesworth · 2 years, 1 month ago

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@Brian Charlesworth Brian Charlesworth Michael Mendrin Check this out. :) Nihar Mahajan · 2 years, 1 month ago

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@Brian Charlesworth I agree, Alex Li should explain his "correct answer" to that one. But I guess I'll have to discuss this only in the View Reports section, and not here. Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin Great. Thanks for checking it out. Your report makes a pretty clear-cut case. Brian Charlesworth · 2 years, 1 month ago

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@Brian Charlesworth Okay, 248 de-nominated. Michael Mendrin · 2 years, 1 month ago

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I have considered 49, for many non-mathematical people kind of forget that it's a prime number. Timothy Wan · 1 year, 6 months ago

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Next number I nominate is 226.

I think, visually for me, 226 is the most forgettable number there is less than 300. It looks like a classroom number at a school you'd rather forget about. Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin Hahaha That's exactly what that number reminds me of too, and I sure can't remember the course I took in that classroom, either. :)

One curiosity about 226 is that the first three digits of \(\pi^{226}\) are \(226.\) This, along with the entry on record that 226 is the maximum number of permutation patterns that can occur within a 9-element permutation, should be enough to de-nominate 226, (at least in comparison to 298). Brian Charlesworth · 2 years, 1 month ago

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Okay, I nominate 178. Except in connection with the number 196, it's hard to find anything interesting to be said about this one.

178 is a digitally balanced number, as its binary number (10110010) has an equal number of zeros and ones.

Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin 178 does have this interesting property "with 196"

178 squared = 31684 196 squared = 38416

178 cubed = 5639752 196 cubed = 7529536

So, 178 should be "de-nominated" Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin Agreed. For both the squares and the cubes to have this result is pretty cool. (4th powers are a no-go though, although both of them do end in the digits \(56.\)) Brian Charlesworth · 2 years, 1 month ago

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Well, maybe we each can nominate more than one candidate. The first I will nominate myself would be 122, since I couldn't think of anything else except that Emperor Hadrian ordered that wall that today bears his name.

However, there are very few known examples of three relatively prime integers, of which different powers of two sum to yet another power of the third. Here is one.

\({ 3 }^{ 5 }+{ 11 }^{ 4 }={ 122 }^{ 2 }\)

so I withdraw 122 from nomination and look for another. Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin \(122_{10}+3_{10} = 11122_3\)

122 is a number \(n\) where the trailing digits of \((n_{10}+b_{10})\) in base \(b\) is \(n\) itself. Garrett Clarke · 2 years, 1 month ago

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@Garrett Clarke Yet another interesting property of 122:

122 squared = 14884, while 221 square = 48841 Michael Mendrin · 2 years, 1 month ago

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@Michael Mendrin You can certainly nominate more than one candidate. Just make sure to start them off in a new comment. Calvin Lin Staff · 2 years, 1 month ago

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249

249 is a major highway in Texas.

Garrett Clarke · 2 years, 1 month ago

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@Garrett Clarke The amazing about this note is that you can always find something interesting if you just look hard enough. 249 is the smallest 3-digit number such that \(249^{2n} = 1 \pmod{10^3}\). This means that 249 raised to any positive integer will either end in \(\underline{001}\) or \(\underline{249}\). Garrett Clarke · 2 years, 1 month ago

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@Garrett Clarke I propose that 249 be de-nominated. Michael Mendrin · 2 years, 1 month ago

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@Garrett Clarke That is part of the point :) Calvin Lin Staff · 2 years, 1 month ago

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@Calvin Lin Any of us is free to find the most interesting things about any "boring" number that's been nominated, i.e., we're free to try shooting down the status of such numbers being boring. Then it's the last man...uh, number standing that wins--the one nobody can come up with anything truly special. Michael Mendrin · 2 years, 1 month ago

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37 Sachin Sharma · 8 months, 3 weeks ago

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Comment deleted Jul 31, 2015

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@Michael Mendrin 284 has been nominated by Alex Li, so I'm deleting this comment. Calvin Lin Staff · 2 years, 1 month ago

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284

Another year, another emperor.... In 284 A.D., Emperor Numerian, (who had succeeded his father Carus, (who died tragically after an unfortunate encounter with a bolt of lightning), the previous year), while traveling in a closed litter through Asia Minor on the way home to Rome, (to which all roads lead), found himself suddenly afflicted with an inflammation of the eyes. Upon return and after opening his litter, his decaying corpse was found. All hail Emperor Diocletian, who promptly blamed Arrius Aper, (a rival for the throne), for Numerian's death and had him executed on the spot. Apparently Diocletian and Arrius weren't that amicable, unlike ...

284 and 220 which together form the smallest amicable pair.

Alex Li · 2 years, 1 month ago

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@Alex Li \(284\) is a component of the smallest amicable pair. Brian Charlesworth · 2 years, 1 month ago

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