A347333 - OEIS

%I #22 Sep 07 2021 13:50:35

%S 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,

%T 20,67,191,36,26,28,31,30,52,68,192,37,38,29,32,34,47,54,69,193,494,

%U 39,41,33,35,48,55,61,70,194,495,78,42,43,40,49,56,62,71,112

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

%C 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:

%C    2  3

%C    4  8 (square with 2^2 terms summing up to 17)

%C The next filling starts with 3:

%C    2  3  5  6

%C    4  8  7  9

%C      10 11 12 (square with 3^2 terms summing up to 71)

%C The next filling starts with 4:

%C    2  3  5  6

%C    4  8  7  9

%C   13 10 11 12

%C   14 15 16 17

%C   18 19 20 30 (square with 4^2 terms summing up to 233)

%C The next filling starts with 5:

%C    2  3  5  6 21 22 23

%C    4  8  7  9 24 25 26

%C   13 10 11 12 27 28 29

%C   14 15 16 17 31 32 33

%C   18 19 20 30 34 35 40 (square with 5^2 terms summing up to 563); etc.

%C 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.

%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2021/08/squares-for-scott.html">Squares for Scott</a>.

%H Scott R. Shannon, <a href="/A347333/a347333.txt">The quarter board when n = 200</a>.

%Y Cf. A347334.

%K base,nonn,tabl

%O 1,1

%A _Eric Angelini_ and _Scott R. Shannon_, Aug 28 2021