[seqfan] Two thingies with digits

[Eric Angelini]

 Hello SeqFans,
 First, could someone please compute a hundred or so terms of S
 where two consecutive terms of S share no digit with their sum?
 This is http://oeis.org/A129562 dropping the "increasing" cons-

 traint. I guess S starts:
 S = 1,2,3,4,5,6,7,8,9,11,13,14,15,17,16,18,12,21...
 Note that S is now a permutation of N. (Hope I didn't overlook S
 in the OEIS.)

 Second, could someone please also compute T, another permutation
 of N, where the sum of the digits of a(n) "starts" a(n+1)?

 I think that T looks like this:
 T = 1,10,11,2,20,21,3,30,31,4,40,41,5,50,51,6,60,61,7,70,71,8,80,

     81,9,90,91,100,12,32,52,72,92,110,22,42,...

Best,

have a nice "Ferragosto",

É.