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exponential factorial
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(Definition)
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Given a positive integer $n$ , the "power tower" $n^{(n - 1)^{(n - 2) \dots }}$ is the exponential factorial of $n$ . The recurrence relation is $a_1 = 1$ , $a_n = n^{a_{n - 1}}$ for $n > 1$ .
So for example, $9 = 3^{2^1}$ , $262144 = 4^{3^{2^1}}$ . The exponential factorial for 5 has almost two hundred thousand base 10 digits. The ones that are small enough are listed in sequence A049384 of Sloane's OEIS.
The sum of the reciprocals of the exponential factorials is a Liouville number. $$\sum_{i = 1}^\infty {1 \over a_i} \approx 1.6111149258083767361111111$$
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"exponential factorial" is owned by CompositeFan.
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Cross-references: Liouville number, reciprocals, sum, OEIS, sequence, digits, base, thousand, hundred, recurrence relation, power, integer, positive
There is 1 reference to this entry.
This is version 4 of exponential factorial, born on 2006-06-20, modified 2006-06-22.
Object id is 8068, canonical name is ExponentialFactorial.
Accessed 1549 times total.
Classification:
| AMS MSC: | 05A10 (Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions) |
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Pending Errata and Addenda
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