[seqfan] Re: I searched for: n^(n-1) = (n-1)^n and n^(n+1) = (n+1)^n

[Rick Shepherd]

...and, in general, it's only necessary to include the "." to search for
constants, without inserting commas in the search string.  In other words,
this works (and would have found the sequence even if it were missing the
cons keyword):

http://www.research.att.com/~njas/sequences/?q=.293166287411861031508028291250805864372&sort=0&fmt=0&language=english&go=Search

(I, too, find such constants interesting, by the way, and would encourage
you to look for others.)

Rick


On Thu, Jun 17, 2010 at 12:42 PM, <franktaw at netscape.net> wrote:

> Check out A085846.
>
> Your search of OEIS is looking for
> 293166287411861031508028291250805864372, not 2,9,3,1,6,6,....
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Daniel Forgues <squid at zensearch.com>
>
> I searched for:
>
>    n^(n-1) = (n-1)^n
>    n^(n+1) = (n+1)^n
>
> with Wolfram Alpha:
>
> [http://www.wolframalpha.com/input/?i=n^%28n-1%29+%3D+%28n-1%29^n
> n^(n-1) =
> (n-1)^n]
> [http://www.wolframalpha.com/input/?i=n^%28n%2B1%29+%3D+%28n%2B1%29^n
> n^(n+1) =
> (n+1)^n]
>
> and got:
>
> n ~~ 3.293166287411861031508028291250805864372257290327121...
> n ~~ 2.293166287411861031508028291250805864372257290327121...
>
> which have the same decimal expansions (only offset of 1, obviously
> expected.)
>
> I checked:
>
> [http://oldweb.cecm.sfu.ca/cgi-bin/isc/lookup?number=3.293166287411861031
> 508028291250&lookup_type=simple
> ISC]
>
> [http://bootes.math.uqam.ca/cgi-bin/ipcgi/lookup.pl?Submit=GO+&number=2.2
> 93166287411861031508028291250&lookup_type=simple
> Plouffe's Inverter]
>
> [http://www.research.att.com/~njas/sequences/?q=2931662874118610315080282
> 91250805864372&sort=0&fmt=0&language=english&go=Search
> OEIS]
>
> And
>
> n ~~ 3.293166287411861031508028291250805864372257290327121...
> n ~~ 2.293166287411861031508028291250805864372257290327121...
>
> are not in ISC, Plouffe's Inverter, OEIS...
>
> Are these 2 related equations with their related (probably
> transcendental...)
> constants mathematically insignificant/uninteresting? Anybody ever
> looked for
> this?  I didn't find anything online about it, is it worth
> investigating?
>
> I just happened to like the symmetrical form of those equations:
>
>    n^(n-1) = (n-1)^n
>    n^(n+1) = (n+1)^n
>
> Thanks
>
> Daniel Forgues
>
>
>
>
>
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