[seqfan] Re: "What primes P have P^P containing the string 'P' as substring'?"

[Leroy Quet]

Is the base-2 version in the EIS? What about, not limited to primes, the sequence of all n where n is a substring in n^n, for the bases 2 through 10?

Thanks,
Leroy Quet

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--- On Mon, 4/26/10, Jonathan Post <jvospost3 at gmail.com> wrote:

> From: Jonathan Post <jvospost3 at gmail.com>
> Subject: [seqfan] "What primes P have P^P containing the string 'P' as substring'?"
> To: "JM Bergot" <thekingfishb at yahoo.ca>, "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Monday, April 26, 2010, 8:07 PM
> JM Bergot asked me in an email: "What
> primes P have P^P containing the
> string 'P' as substring'?"
> 
> 5^5 = 3125 has "5" as substring.
> 
> 11^11 = 285311670611 has two substrings of "11"
> 
> 17^17 = 827240261886336764177  has "17" as 3rd and 2nd
> digit from right-hand.
> 
> 19^19 = 1978419655660313589123979 has a "19" as its left
> end, and another later.
> 
> 31^31 = 17069174130723235958610643029059314756044734431
> 
> has a "31" at right-hand end, and a second to the left a
> ways.
> 
> A051674 (n-th prime)^(n-th prime).
> 
> Is there a sequence in there, base and prime related,
> struggling to be
> interesting to anyone on seqfans?
> 
> Eventually, all P^P are pandigital.  But not "normal."
> Right?
> 
> Best,
> 
> Jonathan Vos Post
> 
> 
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