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A factorial pattern (Posted on 2024-03-03)

22!, 23!, 24! have 22, 23, and 24 digits.

266!, 267!, 268! have 2*266, 2*267, and 2*268 digits.

2712! and 2713! have 3*2712 and 3*2713 digits.

Continue this pattern and you will notice a curious pattern related to a famous number.

Explain the result.

No Solution Yet Submitted by Jer

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looks like ...

| Comment 1 of 2

The pattern continues:

1 1

22 1

23 1

24 1

266 2

267 2

268 2

2712 3

2713 3

27175 4

27176 4

271819 5

271820 5

271821 5

2718272 6

2718273 6

The digits appear to be approaching the digits of e

2.718281828459045

The first part of Stirling's formula is

ln(n!) = n*(ln(n) - 1)

The LHS is related to the number of digits of ln(n)

The RHS is n times something.

Posted by Larry on 2024-03-03 12:16:42

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