

A347333


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


2



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
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OFFSET

1,1


COMMENTS

The quarter board is lexicographically filled with distinct terms, starting in the upperleft 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: A291295 A222431 A291297 * A050024 A182153 A230771
Adjacent sequences: A347329 A347330 A347331 * A347334 A347335 A347336


KEYWORD

base,nonn,tabl


AUTHOR

Eric Angelini and Scott R. Shannon, Aug 28 2021


STATUS

approved



