[seqfan] An "add or make the absolute difference" array

[Eric Angelini]

Hello SeqFans,
could someone check and extend this seq (if of interest)?
[Requires lots of memory]

S = 1, 2, 4, 7, 8, 10, 13, 12, 16, 20, 19, ...

The idea:
- to put all the Naturals in an array, exactly once.
The array rule:
- if you take 2 neighboring integers anywhere in the array,
  their sum or their absolute difference is on the line below,
  between them.
The construction:
- Start the uppermost row with "1"
- extend the uppermost row with the "smallest integer not yet
  present in the array and not leading to a contradiction",
  checking first if the absolute difference between the new 
  integer and its left neighbor is not yet present in the array
  -- else checking if the new integer can be added to its left
  neighbor with no subsequent "damage" either (the result --
  subtraction or addition -- will be written on the line below,
  between the two integers, starting an anti-diagonal)
- complete the said anti-diagonal in the same way, then extend 
  the uppermost row with a new integer.

1 2  4   7    8    10    13    12    16    20  19
 3 6   11  15   18    23    25    28    36   39
  9  5   26  33    41    48    53    64    75
   14  21  59   74    89    101   117   139
     35  38  133   163   190   218   256
       73  95   30    353   408   474
         22  65    323    55   66
           43   258   268   121 
             215   526   147
Best,           311   379
É.                 68