Wandering clock

[Eric Angelini]

Hello math-fun ans seqfan [crossposted to rec.puzzles]

This should look like an ordinary clock (without hands) :

        12
     11     1
   10         2
  9             3
    8         4
      7     5
         6

Consider the 15 digits above and imagine them suddenly
moving clockwise to another place on the clock:
  --> the "1" digits move 1 step clockwise;
  --> the "2" digits move 2 steps clockwise;
  --> the "3" digit moves 3 steps clockwise;
      etc.

A « jump » sees the 14 digits moving simultaneously,
accordingly to their nature (0, the 15th digit, never
moves, of course).

So after jump 1 we would have this configuration (digits
on the same place assemble to form the smallest integer):

        116
     1       1
   50         127
  .              .
    4         28
      .     .
         39

Jump 0 to jump 5 configurations are represented here:


Jump0  1    2    3    4    5    6   7    8    9   10   11    12
Jump1  1  127    .   28    .   39   .    4    .   50    1   116
Jump2 11    1  159    2    .   26   .    .   37    0    .   148
Jump3  1   11    1  147    .    2   .  258    .    0    .   369
Jump4  5    1  113   18    1    6   .   24    9   20    7     .
Jump5  .    .    1   11    1  13579 .    .    .   20    .  2468
...

Question: at what jump will the « jump 0 » configuration
appear again?

Best,
É.

----
ObSeqFan :
We could associate an integer to every jump : it's "horizontal"
sum (81 for jump 0; 366 for jump 1; etc.)

Find the sequence linking jump 0 to jump 0' (same config. again)







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