0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1, 9, ?
What is the next number in the sequence?
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.
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:
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.