[seqfan] Prime stacking on the Tower Of Hanoi

[Daniel Joyce]

High all seqfans.

Prime stacking on the Tower of Hanoi. See the latter
part of this presentation for only readers flamiliar with
the puzzle.

Only for thoughs that are not flamiliar with this puzzle
read the first half of this presentation.

This puzzle in its original form given the least
amount of moves can add up fast as observed below.
With just a total of 3 pegs and (n) number of disks
on post (1) you have to move all of (n) disks one
at a time with the largest disk at the bottom all
the way up to the smallest disk @ the top too post
two or three. Never placing a larger disk on top of
a smaller disk.
The correct number of moves for each (n) number of
disks too move too peg one or peg two is just ---

(2^n)-1

Very simple and the number correct moves for each (n) can
grow very large very fast as (n) grows.

The key being, # 1 disk has to be played in the right
order every other move.

Number 1 disk every other move too post 1,3,2,1,3,2,1...
or 1,2,3,1,2,3,1,2,3,1...this determines what final post
# (2) or (3) the entire stack is moved too.
----------------------------------------------------------

Now getting to the new rules to accomadate all the
primes which I call ---

Prime stacking on The Tower Of Hanoi.

Same rules apply except for the number of pegs.
The number of prime pegs is determined on the next
prime disks after disk 3.
When moving a stack of largest to the smallest disk
(smallest @ top of tower) to another peg moving
one piece at a time and at no time placing a larger
disk on a smaller one in the process.

The new rule added below.
Starting with disk 5 and peg 3 on the next set change
disk 5 to peg 5 and 7 disk making the next set
7 disk and 5 pegs and so on as observed below.
.

2 disk  3 pegs = 3 least possible number of moves.
3 disk  3 pegs = 7 "      "        "     "    "
5 disk  3 pegs = 31 "      "        "     "    "
7 disk  5 pegs = 19 "      "        "     "    "
11 disks 7 pegs = 31 "      "        "     "    "
13 disks 11 pegs = 31 "      "        "     "    "
17 disk  13 pegs = 43 "      "        "     "    "
19 disk  17 pegs = 43 "      "        "     "    "
23 disk  19 pegs = ???

Starting with 7 disk and 5 pegs, one or more of these could be a
wrong number of least amount of moves.

So the new sequence representing the least possible number of
moves =
3,7,31,19,31,31,43,43,...

I am still trying different algorithms and so far I have only
reached 19 disks and 17 pegs = 43 least possible number of moves.


Quite small compared to the original of 2^19 -1 moves, which by
the way is a Merrcenne prime.
Anyone that can produce the next term 23 disk and 19 pegs or more
higher prime pairs please submit.

Thanks,

 Dan