the OEIS machine seems to be down
N. J. A. Sloane
njas at research.att.com
Sat Feb 2 06:13:50 CET 2008
Neil,
This is the next term of the expectation:
e(5) = 348722/81
I will try to compute further term(s) soon.
Regards,
Max
On Feb 1, 2008 5:32 PM, N. J. A. Sloane <njas at research.att.com> wrote:
> My former colleague Toby Berger (now at U of Va)
> has been looking at this problem. Has anyone seen
> anything like this before?
>
> %I A134939
> %S A134939 0,2,64,1274,21760
> %N A134939 Consider a 3-pole Tower of Hanoi configuration which begins with n rings on pole 1. Moves are made at random, where the 1-step transition probabilities out of any state are equal. Let e(n) be the expected number of transitions to reach the state in which which all rings are on pole 3. Sequence gives a(n), the numerator of e(n).
> %C A134939 Both allowable transitions out of any of the three special states in which all the rings are on one of the poles have probabilty 1/2, and each of the three allowable transitions out of any of the other 3^n - 3 states have probabilty 1/3.
> %C A134939 It appears that the denominator of e(n) for n>=1 is 3^(n-1).
> %e A134939 The values of e(0), ..., e(4) are 0, 2, 64/3, 1274/9, 21760/27.
> %K A134939 nonn,frac,more,new
> %Y A134939 Cf. A134940.
> %O A134939 0,2
> %A A134939 Toby Berger (tb6n(AT)virginia.edu), Jan 23 2008
>
> Neil
>
>
Dear Seqfans, (The OEIS machine is still down)
Back in 2005 there was a discussion which began like this (I've edited
it a bit):
The number N=325648 might be called a self-power
number because:
"3" means "a cube is visible in N"
"2" means "a square is visible in N"
"5" means "a power 5 is visible in N"
"6" means "a power 6 is visible in N"
"4" means "a power 4 is visible in N"
"8" means "a power 8 is visible in N"
N=832564 is a SPN too, of course.
["visible" means "as a whole": "25" is
NOT visible in 235]
Question:
Can someone compute all such SPN _which
don't include any 0's or 1's_ ?
This restriction applies because 0^a=0
and 1^b=1, which brings a lot of unwan-
ted SPN like 117 or 308:
"1" means "a power 1 is visible in N"
"7" means "a power 7 is visible in N"
or
"3" means "a cube is visible in N"
"0" means "a power 0 is visible in N"
"8" means "a power 8 is visible in N"
Best,
Eric
_______________________________________________
Eric Angelini wrote:
> Question:
> Can someone compute all such SPN _which
> don't include any 0's or 1's_ ?
There are an infinite number of course...
For example, any sequence of digits 2-9 which contains this
Showing this is an SPN is left as an exercise for the reader.
-------------------------------------
>From njas at research.att.com Wed Jul 6 15:47:33 2005
Dear Seqfans, There were a bunch of messages yesterday
about Self-powers numbers (SPN). But it looks like
no one has yet submitted the sequence to the OEIS!
Would someone kindly work out the first few terms
and send it in?
Thanks!
NJAS
-------------------------------------------
Feb 02 2008: Would someone kindly work out the first few SPN's
and send them to me? Better use email, the OEIS machine is down.
Neil
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