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A330339
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Boustrophedon primes: write the numbers 0, 1, 2, 3, ... in a triangle on a square grid in the boustrophedon manner, ending a row when a prime is reached; sequence lists primes that appear in the zeroth column.
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7
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37, 53, 89, 113, 3821, 3989, 4657, 28661, 29021, 41641, 41669, 44249, 50909, 56053, 57041, 57301, 133981, 16501361, 46178761, 47633441, 47633477, 47722049, 47736121, 47774621, 47803477, 47810209, 47835013, 47835341, 47854969, 47862413, 47865017, 49448573, 49448617
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OFFSET
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1,1
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COMMENTS
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Eric Angelini's illustration shows the first 19 rows of the triangle. Each row ends when a prime is reached, and the next row starts directly under this prime but moves in the opposite direction.
The extended illustration from Walter Trump resembles a giant ski run.
Hans Havermann's plots of A330545, linked here, extend Walter Trump's graph to 4*10^8 rows (probably the longest ski run in the world). Only the turns are shown, and the illustration has been turned sideways.
A330545(k) = 0 iff prime(k) is a term of the present sequence. In a sense A330545 and the simpler A330547 are the more fundamental sequences and show the connection between the present problem and the ordinary primes and their alternating sums.
Note that because primes > 2 are odd, a prime can only appear in column 0 at the end of a row that is moving towards the left. A prime appearing in a row moving to the right will always appear in an odd-numbered column (and in particular, not in the zero column).
Furthermore the column number mod 4 uniquely determines the residue class of primes mod 4 in that column. If the column number is 0,1,2,3 mod 4 then the primes in that column are 1,3,3,1 respectively (see the "Notes" link). In particular, a(n) == 1 mod 4. - N. J. A. Sloane, Jan 04 2020
Note that the primes > 2 in column one and two are the primes in A282178.
Note on the links: The illustrations from Angelini and Trump show all the terms 0,1,2,3,4,..., while those of Havermann and Sloane just show the primes (as in A330545).
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LINKS
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CROSSREFS
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A330546 gives the list of indices i such that a(n) = prime(i).
A127596 is another sequence with a similar flavor.
Not to be confused with A000747 = Boustrophedon transform of primes.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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