Pattern

[Eric Angelini]

Hello,
I've just submitted this seq. to OEIS : comments ?
BTW, I've not received any single response to my last
week's question about the definition of a "slowest
increasing sequence" : how many are we on this list ?
Regards,
É.
-------

12 34 56 78 910 1 11 2 131 4 151 6 171 8 1920 212 22 3 242 5 262 7 282 9 303
13 23 33 43 53 63 73 83 940 414 24 344 454 64 74 84 950 515 25 35 45 55 65
75 85 960 616 26 36 46 566 676 86 970 717 27 37 47 57 67 77 87 980 818 28 38
48 58 68 788 8990 919 29 39 49 59 69 79 89 9100 10 110 210 310 410 510 610
710 810 91 101 111...

Write each natural integer >0 on a single label. Put the labels one behind
the other to form an (infinite) line L. Now consider the (infinite) pattern
designed by the lone digits of L -- the pattern starts like this: 1 2 3 4 5
6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 etc. The challenge
is to re-arrange the labels of L in order to reproduce the same pattern. But
the constraints are: (1) a label of L _cannot_ be re-used to represent the
_same_ number as the one it bears (so the label "1" cannot start the new
sequence S; the label "1" will be used to represent a "1" elsewhere in the
sequence S, as for instance in "11") ; (2) when you move a label from L to
build the next term of S, always choose the leftmost available one in L (so
S will start with the label "12" and not with the label "123" or "1234567",
for instance). Labels of L can be used only once for S, of course, because S
is a re-ordering of L's labels; S has the same number of labels as L, but
put in another succession.