[seqfan] a(n)*a(n+1) shows at least twice the same digit

[Eric Angelini]

Hello SeqFans,
we want the lexico-first permutation of the integers > 0 
such that a(n)*a(n+1) shows at least twice the same digit.
If I'm not wrong, here is the lexico-first permutation of
the integers 1 to 38:

S = 1,11,2,22,3,33,10,20,5,23,7,16,9,13,17,15,35,19,6,24,12,21,
25,4,28,8,14,18,29,31,32,34,26,38,30,36,37,27,...

The first products are:
11,22,44,66,99,330,800,100,115,161,... and the last one above
is 37*27=999

Best,
É.
(I guess there are similar permutations 
producing 3 identical digits in the result of
a(n)*a(n+1)*a(n+2), or 4 identical digits in... etc.)