A347333 Square array read by antidiagonals downwards (see Comments for definition).

2, 3, 4, 5, 8, 13, 6, 7, 10, 14, 21, 9, 11, 15, 18, 22, 24, 12, 16, 19, 190, 23, 25, 27, 17, 20, 67, 191, 36, 26, 28, 31, 30, 52, 68, 192, 37, 38, 29, 32, 34, 47, 54, 69, 193, 494, 39, 41, 33, 35, 48, 55, 61, 70, 194, 495, 78, 42, 43, 40, 49, 56, 62, 71, 112

Offset: 1

Author

Eric Angelini and Scott R. Shannon, Aug 28 2021

Keywords

• base
• nonn
• tabl

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

Cf. A347334.