Eric, That reminds me a lot of A327743, although the rules are slightly different On Tue, Mar 31, 2020 at 7:39 PM Éric Angelini <bk263401@skynet.be> wrote:
Hello Math-Fun, have a look here, on my personal page: https://bit.ly/2wGyzpv You will see how to build this array; it starts (fixed font):
A new array for the OEIS?
0 +1 +3 +7 +11 +5 +14 ... -1 +2 -4 +4 -6 +9 ... -3 +6 -8 -10 -15 ... -9 -14 -2 -25 ... -5 -12 -23 ... -7 -35 ... -28 ... ...
The idea is to insert in an infinite “triangular” array, all integers from -∞ to +∞, with no duplicates.
We start, as usual, in the upper left corner with 0. The array now is filled with those two rules:
Rule 1) we always try to extend the upper row with the smallest positive integer a(n) not present so far in A (A is the array), integer that doesn’t lead to a contradiction immediately, or later in the rows below it; Rule 2) a(n) and a(n-1), the term at the left of a(n), produce another integer in the row below them; this term is the difference (smallest term – biggest term). If this leads to a contradiction (immediately or later in the antidiagonal), we try (biggest term – smallest term). If both operations lead to a contradiction, we try a(n)+1 instead of a(n) and repeat the whole process, filling A by antidiagonals.
Example: After 0, we write 1 because this 1 doesn’t lead to a contradiction: we will have -1 below the pair (as 0 – 1 = -1): (...) Best, É.
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