The fact that four is cosmic, at least in English, is quite well discussed.

However, what if we instead took a number and then took the first letter of its word form that number and converted it to its alphabetical placing to generate a sequence?

Your job is to:

1) Find three numbers which generate its own cyclic sequence.

2) Even more special, find the number which just repeats itself. (i.e. the cosmic number of this sequence)

3) Any other cyclic number(s) that I may have missed (or a 'proof' that there are no others).


1 Answer 1


Definitely an interesting variant on the original- I believe I have answers to the first two, and still thinking on the third.


Nineteen goes to N(fourteen), which goes to F(six), which goes to S(nineteen)


T is at position twenty, so goes back to itself.


Added proof by f'':
Every number must go to a number from 1 to 26, so these are the only numbers that can possibly be in cycles. It is simple to check that all 26 start with one of the letters efnost. t loops to itself, nfs form a cycle, and eo both go to f.

  • $\begingroup$ Quite easy, I suppose. I'll see if you can show how there are no more cyclic numbers, but I'll accept this one anyway. $\endgroup$
    – Inazuma
    Commented Jun 12, 2016 at 2:56

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