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Here is a list of numerical sequences:

  • 1, 3, 5, 4
  • 2, 3, 5, 4
  • 3, 5, 4
  • 4
  • 5, 4
  • 6, 3, 5, 4
  • ...and so on.

(1 is 3 and 2 is 3, but 1 is not 2 and 2 is not 1. The same rule applies to every number in the sequence.)

There is a simple rule that governs these sequences. What is it?
Use spoiler tags in your answer, please.

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The rule is...

The next number in the sequence is the number of characters in the previous number when spelled out.
Each of the sequences end on 4 because it has 4 characters and the sequence is then essentially eternal.

Let's take a look at the first sequence:

1: 'o' + 'n' + 'e' = 3
3: 't' + 'h' + 'r' + 'e' + 'e' = 5
5: 'f' + 'i' + 'v' + 'e' = 4
And 4 goes on forever so it is terminal.

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