What’s Next?: An Unorthodox Number Sequence

numbers

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.

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My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

20 thoughts on “What’s Next?: An Unorthodox Number Sequence

  1. 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! 😜

    Liked by 2 people

  2. 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.

    Liked by 2 people

    1. 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…

      Liked by 1 person

  3. “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….?

    Liked by 2 people

    1. 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.

      Like

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