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itachi-san
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The answer is

is

Spoiler for I knew this:

is

Spoiler for I knew this:

5000 because

The Series is a series of "Nonnegative integers that when written out in full in English have no repeated letter." :rolleyes:

You borrowed it from The On-Line Encyclopedia of Integer Sequences!

:lol:

I had Already visited this site. B))

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1, 2, 4, 5, 6, 8, 10, 40, 46, 60, 61, 64, 80, 84, ?

What is the next number in the series and why?

Is the series infinite or finite?

Edited by frotorious
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Is the series infinite or finite?

That is an interesting question, but the series is definitely finite. In fact it has an upper bounds cardinality (I think) of the summation from 1 to n of n^n. i.e. 1^1 + 2^2 + ... + 26^26. This seems a little strange but it is derived from.

26 one letter numbers

26*25 two letter numbers

...

26! twenty-six letter numbers

What doesn't seem strange, though:

There are only so many combinations you can make out of 26 letters without repeating a letter.

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Sorry, wish I could edit that last post to get the blatantly wrong formula off, but this will have to do.

That is an interesting question, but the series is definitely finite. In fact it has an upper bounds cardinality (I think) of the summation from n = 0 to 25 of 26!/n!. i.e. 26 + 26*25 + ... + 26!. This seems a little strange but it is derived from.

26 one letter numbers

26*25 two letter numbers

...

26! twenty-six letter numbers

What doesn't seem strange, though:

There are only so many combinations you can make out of 26 letters without repeating a letter.

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