OFFSET
1,1
COMMENTS
The quarter board is lexicographically filled with distinct terms, starting in the upper-left corner with 2 (as 1 is not a prime number); we then form a square of side 2 whose terms sum up to a prime:
2 3
4 8 (square with 2^2 terms summing up to 17)
The next filling starts with 3:
2 3 5 6
4 8 7 9
10 11 12 (square with 3^2 terms summing up to 71)
The next filling starts with 4:
2 3 5 6
4 8 7 9
13 10 11 12
14 15 16 17
18 19 20 30 (square with 4^2 terms summing up to 233)
The next filling starts with 5:
2 3 5 6 21 22 23
4 8 7 9 24 25 26
13 10 11 12 27 28 29
14 15 16 17 31 32 33
18 19 20 30 34 35 40 (square with 5^2 terms summing up to 563); etc.
Reading at this stage the quarter board by its antidiagonals gives: 2, 3, 4, 5, 8, 13, 6, 7, 10, 14, 21, 9, 11, 15, 18, 23, 25, ... which is precisely this sequence.
LINKS
Eric Angelini, Squares for Scott.
Scott R. Shannon, The quarter board when n = 200.
CROSSREFS
KEYWORD
AUTHOR
Eric Angelini and Scott R. Shannon, Aug 28 2021
STATUS
approved