[seqfan] More fractal triangles

[Eric Angelini]

Hello SeqFans,
Erase from S all pairs of integer [a(i), a(i+1)] having the
same parity --like (2,4) or (3,5)-- and you'll get S back.

S = 1,2,4,3,5,2,7,9,4,3,6,8,5,2,7,10,12,9,4,3,6,11,13,8,5,2,7,10,15,17,12,9,4,3,6,11,14,16,13,8,5,2,7,10,15,18,20,17,12,9,4,3,6,11,14,19,21,16,13,8,5,2,7,10,15,18,23,25,20,17,12,9,4,3,6,11,14,19,22,24,21,16,13,8,5,2,7,10,15,18,23,26,28,25,20,17,12,9,4,3,6,11,14,19,22,27,29,...


The generating triangles [after a(1)=1] are:

1            2                                4,3
           5,2,7                            9,4,3,6
         8,5,2,7,10                      12,9,4,3,6,11
      13,8,5,2,7,10,15                17,12,9,4,3,6,11,14
   16,13,8,5,2,7,10,15,18          20,17,12,9,4,3,6,11,14,19
21,16,13,8,5,2,7,10,15,18,23    25,20,17,12,9,4,3,6,11,14,19,22
            ...                               ...

Read horizontally, line after line, to see S.
Best,
É.