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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 (list; table; graph; refs; listen; history; text; internal format)
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: 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

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Last modified October 17 07:39 EDT 2021. Contains 348048 sequences. (Running on oeis4.)