What is the smallest uninteresting (natural) number? I’d run across this question before it first appeared in TV program QI.

One approach is to say “all natural numbers are interesting”, so there are no uninteresting numbers. Indeed, the On-Line Encyclopedia of Integer Sequences (OEIS) has sequence number 27, which is the natural numbers. But this approach doesn’t work. The OEIS list of natural numbers stops at number 77, so says in effect that “77 is interesting as the 77th natural number” but “78 is not interesting as the 78th natural number”. For 78 to be interesting it has to be in some other sequence of numbers, and it is, currently in 14418 other sequences.

Another approach is to say, “if a number is the smallest uninteresting number then that in itself makes it interesting”. So if it’s not interesting then it is interesting and vice versa. Again, this approach doesn’t work, because more numbers are added to the collection of interesting numbers all the time.So “the smallest natural number” is only a transitory phenomenon.

Let’s look at the smallest uninteresting number from a historical perspective.

14 is the first uninteresting number, according to Weird Al Yankovic. Other early claims include:
39 is the first uninteresting number, in the 1986 first edition of “The Penguin Dictionary of Curious and Interesting Numbers” by David Wells.
51, in the second edition of the same book.
338, from the webpage http://math.crg4.com/uninteresting.html, 2006 version.
488, ditto 2009 version.

None of the above five numbers are based on the lists in the OEIS. Claims for the first uninteresting number based on non-appearance in the OEIS start with:

8795, by Ingo Althofer in March 2008.

11630, by Nathaniel Johnson in June 2009.
This contribution is recognised by the OEIS itself. 11630 is the fifth number in the sequence a(n) = (n^6 + 2n^5 + 2n^4 + n^3 + 2n)/2. and the comment is “Before this sequence, 11630 was an uninteresting number.
But now 11630 appears in eight sequences in the OEIS, so is not longer interesting because it is uninteresting.

Other numbers that at one time didn’t appear in the OEIS along with 11630 are 12067, 12407, 12887, 13258, 13794, 13882, 13982, 14018, 14163, 14180, 14194. All these are now interesting.

12067 appears ten times. For example it’s interesting because it’s in the list of “Number of irreducible representations of the symmetric group S_n such that their degree is divisible by 3.”

12407, quite widely quoted on as the smallest uninteresting number, was the smallest uninteresting number from November 2009 until at least November 2011, now it appears seven times, for example as the fourth number in the “Numerator of Hermite(n, 19/26).”

13794 appears eight times. It was the smallest uninteresting number from April 2012 until 2 Nov 2012.

14228 appears four times. It was the smallest uninteresting number from 3 Nov 2012 until at least the start of Apr 2015. It’s interesting as a power of 2 with all the digit 0s suppressed.

14972 appears three times. It was the smallest uninteresting number in Nov 2015 but is no longer uninteresting.

So, what is the smallest uninteresting number now?

mollwollfumble said:

What is the smallest uninteresting (natural) number? I’d run across this question before it first appeared in TV program QI.

One approach is to say “all natural numbers are interesting”, so there are no uninteresting numbers. Indeed, the On-Line Encyclopedia of Integer Sequences (OEIS) has sequence number 27, which is the natural numbers. But this approach doesn’t work. The OEIS list of natural numbers stops at number 77, so says in effect that “77 is interesting as the 77th natural number” but “78 is not interesting as the 78th natural number”. For 78 to be interesting it has to be in some other sequence of numbers, and it is, currently in 14418 other sequences.

Another approach is to say, “if a number is the smallest uninteresting number then that in itself makes it interesting”. So if it’s not interesting then it is interesting and vice versa. Again, this approach doesn’t work, because more numbers are added to the collection of interesting numbers all the time.So “the smallest natural number” is only a transitory phenomenon.

Let’s look at the smallest uninteresting number from a historical perspective.

14 is the first uninteresting number, according to Weird Al Yankovic. Other early claims include:
39 is the first uninteresting number, in the 1986 first edition of “The Penguin Dictionary of Curious and Interesting Numbers” by David Wells.
51, in the second edition of the same book.
338, from the webpage http://math.crg4.com/uninteresting.html, 2006 version.
488, ditto 2009 version.

None of the above five numbers are based on the lists in the OEIS. Claims for the first uninteresting number based on non-appearance in the OEIS start with:

8795, by Ingo Althofer in March 2008.

11630, by Nathaniel Johnson in June 2009.
This contribution is recognised by the OEIS itself. 11630 is the fifth number in the sequence a(n) = (n^6 + 2n^5 + 2n^4 + n^3 + 2n)/2. and the comment is “Before this sequence, 11630 was an uninteresting number.
But now 11630 appears in eight sequences in the OEIS, so is not longer interesting because it is uninteresting.

Other numbers that at one time didn’t appear in the OEIS along with 11630 are 12067, 12407, 12887, 13258, 13794, 13882, 13982, 14018, 14163, 14180, 14194. All these are now interesting.

12067 appears ten times. For example it’s interesting because it’s in the list of “Number of irreducible representations of the symmetric group S_n such that their degree is divisible by 3.”

12407, quite widely quoted on as the smallest uninteresting number, was the smallest uninteresting number from November 2009 until at least November 2011, now it appears seven times, for example as the fourth number in the “Numerator of Hermite(n, 19/26).”

13794 appears eight times. It was the smallest uninteresting number from April 2012 until 2 Nov 2012.

14228 appears four times. It was the smallest uninteresting number from 3 Nov 2012 until at least the start of Apr 2015. It’s interesting as a power of 2 with all the digit 0s suppressed.

14972 appears three times. It was the smallest uninteresting number in Nov 2015 but is no longer uninteresting.

So, what is the smallest uninteresting number now?

See also https://en.wikipedia.org/wiki/Interesting_number_paradox

mollwollfumble said:

Another approach is to say, “if a number is the smallest uninteresting number then that in itself makes it interesting”. So if it’s not interesting then it is interesting and vice versa. Again, this approach doesn’t work, because more numbers are added to the collection of interesting numbers all the time.So “the smallest natural number” is only a transitory phenomenon.

I think it does work. It is a consideration that defeats the concept.

“14 is the first uninteresting number, according to Weird Al Yankovic.”

When such an authority has spoken, surely further debate is pointless.

(Incidentally, before discovering his song “Bob” fairly recently, I don’t think I’d actually seen or heard a weird Al performance, in spite of being well aware of his name. )

The Rev Dodgson said:

“14 is the first uninteresting number, according to Weird Al Yankovic.”

When such an authority has spoken, surely further debate is pointless.

(Incidentally, before discovering his song “Bob” fairly recently, I don’t think I’d actually seen or heard a weird Al performance, in spite of being well aware of his name. )

I think we had a thread on it…

dv said:

The Rev Dodgson said:

“14 is the first uninteresting number, according to Weird Al Yankovic.”

When such an authority has spoken, surely further debate is pointless.

(Incidentally, before discovering his song “Bob” fairly recently, I don’t think I’d actually seen or heard a weird Al performance, in spite of being well aware of his name. )

I think we had a thread on it…

If I had a bit more time I’d come up with a palindromic reply, but I’ve got a plane to catch.

dv said:

mollwollfumble said:

Another approach is to say, “if a number is the smallest uninteresting number then that in itself makes it interesting”. So if it’s not interesting then it is interesting and vice versa. Again, this approach doesn’t work, because more numbers are added to the collection of interesting numbers all the time.So “the smallest natural number” is only a transitory phenomenon.

I think it does work. It is a consideration that defeats the concept.

I don’t think so, because once mathematics proves something it sticks forever, but the concept of “smallest uninteresting number” is transient.

Looking forward from largest previous known smallest uninteresting number I had to LOL at this.

15167 = Number of alkyl derivatives of acetylene with 15 carbon atoms.

The universe precludes the possibility of uninteresting numbers

dv said:

The universe precludes the possibility of uninteresting numbers

i like this.

sarahs mum said:

dv said:

The universe precludes the possibility of uninteresting numbers

i like this.

Sure, but prove it. Every interesting number must be less than the 77th item in any series. Sometimes much less. For example “a(n+1) = 2^a(n)” is interesting only for n<=5.

I have just realised that this question is yet another example of the problems caused by either/orism.

Being “interesting” is not an either/or property, it is a continuum, and there is no number of exactly zero interest.

If we wanted to determine the smallest number of negligible interest we would need some way of putting a numerical value to the level of interest, and then set some arbitrary value as being negligible.

But even that assumes that the level of interest is constant, but in fact the act of evaluating the interest of a number changes the level of interest, so determining the number would be an infinitely recursive process, that would ensure that not only was there no number of zero interest, there was also no number of negligible interest (unless we somehow managed to define being of negligible interest as a fact of negligible interest).

> we would need some way of putting a numerical value to the level of interest, and then set some arbitrary value as being negligible.

Exactly, the standard way now is to use a top-hap filter to (fairly) arbitrarily decide where the cut-off point is. Not every number can be interesting because the number of numbers is infinite but the number of people is finite. So there will always be an infinite number of uninteresting numbers.

It seems to me that both “interesting” and “uninteresting” need formal definition in relation to this discussion. Using dictionary definitions, all numbers are interesting to me.

mollwollfumble said:

> we would need some way of putting a numerical value to the level of interest, and then set some arbitrary value as being negligible.

Exactly, the standard way now is to use a top-hap filter to (fairly) arbitrarily decide where the cut-off point is. Not every number can be interesting because the number of numbers is infinite but the number of people is finite. So there will always be an infinite number of uninteresting numbers.

I disagree. The number of interesting numbers is not limited to the number of people, or even to the number of living organisms capable of considering the problem multiplied by the number of time periods taken to analyse one number for interestingness in an average life.

mollwollfumble said:

What is the smallest uninteresting (natural) number? I’d run across this question before it first appeared in TV program QI.
…
Let’s look at the smallest uninteresting number from a historical perspective.

14 is the first uninteresting number, according to Weird Al Yankovic. Other early claims include:
…
12407, quite widely quoted on as the smallest uninteresting number, was the smallest uninteresting number from November 2009 until at least November 2011, now it appears seven times, for example as the fourth number in the “Numerator of Hermite(n, 19/26).”

13794 appears eight times. It was the smallest uninteresting number from April 2012 until 2 Nov 2012.

14228 appears four times. It was the smallest uninteresting number from 3 Nov 2012 until at least the start of Apr 2015. It’s interesting as a power of 2 with all the digit 0s suppressed.

14972 appears three times. It was the smallest uninteresting number in Nov 2015 but is no longer uninteresting.

So, what is the smallest uninteresting number now?

I’ve been searching forwards. The smallest uninteresting number must be greater than 16000.

What if there is a largest uninteresting number, and it is smaller than the smallest uninteresting number?

So where does the expression “That’s interesting” come from?

The Rev Dodgson said:

What if there is a largest uninteresting number, and it is smaller than the smallest uninteresting number?

That would be very interesting!

bob(from black rock) said:

The Rev Dodgson said:

What if there is a largest uninteresting number, and it is smaller than the smallest uninteresting number?

That would be very interesting!

And thus rule itself out of the uninteresting number competition.

Tamb said:

bob(from black rock) said:

The Rev Dodgson said:

What if there is a largest uninteresting number, and it is smaller than the smallest uninteresting number?

That would be very interesting!

And thus rule itself out of the uninteresting number competition.

Now that’s VERY interesting

mollwollfumble said:

mollwollfumble said:

What is the smallest uninteresting (natural) number? I’d run across this question before it first appeared in TV program QI.
…
Let’s look at the smallest uninteresting number from a historical perspective.
…
So, what is the smallest uninteresting number now?

I’ve been searching forwards. The smallest uninteresting number must be greater than 16000.

Continuing the search. The smallest uninteresting number must be greater than 17000.

Question for Rev D. What is the smallest number that is interesting for only one reason?

mollwollfumble said:

mollwollfumble said:

mollwollfumble said:

What is the smallest uninteresting (natural) number? I’d run across this question before it first appeared in TV program QI.
…
Let’s look at the smallest uninteresting number from a historical perspective.
…
So, what is the smallest uninteresting number now?

I’ve been searching forwards. The smallest uninteresting number must be greater than 16000.

Continuing the search. The smallest uninteresting number must be greater than 17000.

Question for Rev D. What is the smallest number that is interesting for only one reason?

Well, that was unexpected. I’ve found a number that is half uninteresting.

The number is 17843.

Is there a precise definition of an interesting number? That is, is there a specific test that can be applied to a given number to unequivocally determine if it’s interesting. It seems to me that the notion of an interesting number is flawed because the concept of interestingness is imprecise.

funny question

probably eleven, because it’s at that point I run out of fingers and thumbs

it’s 0

// there is no number of exactly zero interest.

except 0

KJW said:

Is there a precise definition of an interesting number? That is, is there a specific test that can be applied to a given number to unequivocally determine if it’s interesting. It seems to me that the notion of an interesting number is flawed because the concept of interestingness is imprecise.

Yes. The precise definition is “Appearance on the oeis website” or “Appearance in a sequence on the oeis website”. The ambiguity allows 17843 to be semi-uninteresting.

I’ve found the smallest uninteresting number. It’s 18159. I’ve modified Wikipedia to include it.

As for my other question, “What is the smallest natural number to be interesting for only one reason”, I’ve found the answer, it’s 17439.

mollwollfumble said:

KJW said:

Is there a precise definition of an interesting number? That is, is there a specific test that can be applied to a given number to unequivocally determine if it’s interesting. It seems to me that the notion of an interesting number is flawed because the concept of interestingness is imprecise.

Yes. The precise definition is “Appearance on the oeis website” or “Appearance in a sequence on the oeis website”. The ambiguity allows 17843 to be semi-uninteresting.

I’ve found the smallest uninteresting number. It’s 18159. I’ve modified Wikipedia to include it.

As for my other question, “What is the smallest natural number to be interesting for only one reason”, I’ve found the answer, it’s 17439.

It’s lucky you used OEIS as the defining location, rather than Wikipedia:

Deletionists vs Inclusionists

The Rev Dodgson said:

mollwollfumble said:

KJW said:

Is there a precise definition of an interesting number? That is, is there a specific test that can be applied to a given number to unequivocally determine if it’s interesting. It seems to me that the notion of an interesting number is flawed because the concept of interestingness is imprecise.

Yes. The precise definition is “Appearance on the oeis website” or “Appearance in a sequence on the oeis website”. The ambiguity allows 17843 to be semi-uninteresting.

I’ve found the smallest uninteresting number. It’s 18159. I’ve modified Wikipedia to include it.

As for my other question, “What is the smallest natural number to be interesting for only one reason”, I’ve found the answer, it’s 17439.

It’s lucky you used OEIS as the defining location, rather than Wikipedia:

Deletionists vs Inclusionists

:)