0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1, 9, ?

What is the next number in the sequence?

## Solution

At first glance, there seems to be an absence of any logical pattern in the sequence. Even after further examination, it may still baffle you since the pattern is well hidden.

This sequence is actually based on the Roman numerals.

How?

List the English names of numbers 1 through 17 and remove all the letters except for the Roman numerals (I, V, X, and L) as shown below:

ONE

TWO

THREE

FOUR

FIVE

SIX

SEVEN

EIGHT

NINE

TEN

ELEVEN

TWELVE

THIRTEEN

FOURTEEN

FIFTEEN

SIXTEEN

SEVENTEEN

The Roman numerals represent the numbers in the sequence while the words that do not have Roman numerals in them represent 0 in the sequence. It doesn’t matter if the Roman numbers are several letters apart. For example, ELEVEN represents 55 because after you delete the other letters, only L and V remain, i.e. LV or 55.

Therefore, the next number in the sequence is 5 since SEVENTEEN has a V in it which is the Roman numeral for 5.

I found this sequence fortuitously while browsing on OEIS (Online Encyclopedia of Integer Sequences). The sequence was discovered by John H. Conway. In OEIS, this sequence is labeled as A002904.

That seems like the Rube Goldberg way to define a pattern 😳

LikeLiked by 2 people

Ah, I think that I’m one of the only few people over here, who’s not an American, who would get the reference. Here, we use “Heath Robinson” for this kind of thing 🙂

LikeLiked by 1 person

🤔😎

LikeLike

Fascinating! I love that an apparently numerical sequence turns out to be literary and historical😁

LikeLiked by 1 person

Edmark M. Law, thanks! And thanks for sharing your great posts every week!

LikeLiked by 1 person

0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1, 9, ?

I guessed 5, but only because I cut the number sequence down the middle between the 55’s, then went backwards from the second 55, flipping the 2nd and 3rd numbers and the 5th and 6th numbers, and the 8th and 9th numbers, so my sequence would have been

0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55 // 55, 1, 0, 1, 9, 5, 4, 0, 0, 0, 0.

However, doing it with the Roman numerals found in the words (the correct way) the sequence would be

0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1, 9, 55, 55, 9, (SEVENTEEN) 5, (EIGHTEEN) 1, (NINETEEN) 1, (TWENTY) 0.

Close, but no prize! 😜

LikeLiked by 2 people

Well, you at least found some sort of pattern :)

LikeLiked by 1 person

men i dont understand it

LikeLiked by 1 person

A well-hidden pattern indeed! I never had reason to memorize Roman numerals, so I only know the combinations of X, V, and I. Had I had the cleverness to consider a Roman numeral interpretation, I wouldn’t have recognized LV as 55.

LikeLiked by 2 people

The year of publication of several old books are written in Roman numerals. So, my knowledge of it at least has some use. Even if I know the Roman numerals, I’m not certain if I cpuld answer this puzzle…

LikeLiked by 1 person

Some people are soooo smart!

LikeLiked by 1 person

That was a good one!😊 Before I read the solution I got ants in my brain!😁😁😁

LikeLiked by 1 person

｢(ﾟ<ﾟ)ﾞ??

LikeLiked by 2 people

loved this sequence , very interesting!

LikeLiked by 2 people

Thanks for reading.

LikeLiked by 1 person

“this sequence is labeled as A002904.”

Ah yes, I remember it well…good old A002904

I wonder what correspondences can be found between all these sequences and their respective label numbers….?

LikeLiked by 2 people

It’s pretty common for us to reference the sequence labels when corresponding with each other. Mathematicians (well, mostly number theorists) already know where to check, say, if you tell them about sequence A007318.

LikeLike

Wow, I love that.

LikeLiked by 1 person

I didn’t get that one and yet I don’t feel bad about it. Nice puzzle!

LikeLiked by 2 people

Glad you liked it.

LikeLiked by 1 person