List questions from tetration

Published on 11 Jan 2014 - 17:06

677

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Question about tetration modulus a prime $p>100$

Published on 12 Jan 2014 - 23:37

100

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Does $a \uparrow \uparrow (n+1)-a \uparrow \uparrow n$ divide $a \uparrow \uparrow(n+2) - a \uparrow \uparrow(n+1 )$?

Published on 14 Jan 2014 - 11:58

415

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Is tetration a transcendental function?

Published on 25 Mar 2026 - 12:22

168

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Is there a proof that the number $2 \uparrow \uparrow m+3 \uparrow \uparrow n$ is always squarefree?

Published on 19 Jan 2014 - 20:34

456

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Which digit occurs most often?

Published on 25 Mar 2026 - 17:26

302

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Comparison between two tetrations

Published on 01 Feb 2014 - 0:39

218

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Prime factors of $\sum_{k=1}^{30}k^{k^k}$

Published on 11 Feb 2014 - 0:05

1k

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Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic

Published on 13 Feb 2014 - 21:10

1.7k

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Fractional Composite of Functions

Published on 14 Feb 2014 - 10:56

212

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Prime factors of $2^{2^2}+3^{3^3}+5^{5^5}+7^{7^7}$

Published on 19 Feb 2014 - 23:08

163

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Appear the digits in the number $3^{3^{3^3}}$ approximately equally often?

Published on 26 Feb 2014 - 1:08

2.7k

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Last digits of power towers $7$, $7^7$, $7^{7^7}$, $7^{7^{7^7}}$, ... don't change, and generalisation

Published on 05 Mar 2014 - 2:54

135

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$2 \uparrow^n 2 = 4$ and the magnificence of $2$

Published on 09 Mar 2014 - 12:16

1.2k

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Infinite Power Tower

Published on 24 Apr 2017 - 21:38

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Stationary prime factor 34276387 , confirmation and generalization wanted.

Question about tetration modulus a prime $p>100$

Does $a \uparrow \uparrow (n+1)-a \uparrow \uparrow n$ divide $a \uparrow \uparrow(n+2) - a \uparrow \uparrow(n+1 )$?

Is tetration a transcendental function?

Is there a proof that the number $2 \uparrow \uparrow m+3 \uparrow \uparrow n$ is always squarefree?

Which digit occurs most often?

Comparison between two tetrations

Prime factors of $\sum_{k=1}^{30}k^{k^k}$

Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic

Fractional Composite of Functions

Prime factors of $2^{2^2}+3^{3^3}+5^{5^5}+7^{7^7}$

Appear the digits in the number $3^{3^{3^3}}$ approximately equally often?

Last digits of power towers $7$, $7^7$, $7^{7^7}$, $7^{7^{7^7}}$, ... don't change, and generalisation

$2 \uparrow^n 2 = 4$ and the magnificence of $2$

Infinite Power Tower

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