The number 42

[Gerald McGarvey]

Correction: The phi iteration can be repeated 4*42 times for 42^42.
Also, entry A064415 helps explain this
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A064415
so 42 is rather ordinary in this regard.

Gerald

At 08:12 PM 5/1/2005, Gerald McGarvey wrote:

>Some information about the number 42
>
>http://en.wikipedia.org/wiki/42_%28number%29
>
>http://en.wikipedia.org/wiki/The_Answer_to_Life,_the_Universe,_and_Everything
>
>to this I'll add:
>
>cosine(42) ~ -0.399985
>
>
>Let phi_n denote Euler's totient function iterated n times, then
>phi_n(42^42) = 2^(42+n) * 3^42 * 7^(42-n) for n = 1 to 42.
>The phi iteration can be repeated 3*42 times.
>42^42/sum(all resulting phi values) =
>2.49999999999999999999999118906...
>http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A104112 
>
>
>Cheers,
>Gerald
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