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

1,1

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

Table of n, a(n) for n=1..65.

Eric Angelini, Squares for Scott.

Scott R. Shannon, The quarter board when n = 200.

Crossrefs

Cf. A347334.

Sequence in context: A222431 A291297 A373895 * A050024 A182153 A230771

Adjacent sequences: A347330 A347331 A347332 * A347334 A347335 A347336

Keyword

base,nonn,tabl

Author

Eric Angelini and Scott R. Shannon, Aug 28 2021

Status

approved