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A362463
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Array of numbers read by upward antidiagonals: leading row lists the primes as they were in the 19th century (A008578); the following rows give absolute values of differences of previous row.
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1
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1, 1, 2, 0, 1, 3, 1, 1, 2, 5, 0, 1, 0, 2, 7, 1, 1, 2, 2, 4, 11, 0, 1, 2, 0, 2, 2, 13, 1, 1, 2, 0, 0, 2, 4, 17, 0, 1, 2, 0, 0, 0, 2, 2, 19, 1, 1, 2, 0, 0, 0, 0, 2, 4, 23, 0, 1, 2, 0, 0, 0, 0, 0, 2, 6, 29, 1, 1, 0, 2, 2, 2, 2, 2, 2, 4, 2, 31, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 4, 6, 37, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 4, 41
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OFFSET
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1,3
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COMMENTS
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Analogous to A036262. The Gilbreath conjecture is that the initial terms of the rows are 1,(1,0)* = A135528.
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LINKS
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N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)
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EXAMPLE
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The array begins:
1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67
1 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4
0 1 0 2 2 2 2 2 2 4 4 2 2 2 2 0 4 4 2 2
1 1 2 0 0 0 0 0 2 0 2 0 0 0 2 4 0 2 0 2
0 1 2 0 0 0 0 2 2 2 2 0 0 2 2 4 2 2 2 0
1 1 2 0 0 0 2 0 0 0 2 0 2 0 2 2 0 0 2 2
0 1 2 0 0 2 2 0 0 2 2 2 2 2 0 2 0 2 0 0
1 1 2 0 2 0 2 0 2 0 0 0 0 2 2 2 2 2 0 0
0 1 2 2 2 2 2 2 2 0 0 0 2 0 0 0 0 2 0 0
1 1 0 0 0 0 0 0 2 0 0 2 2 0 0 0 2 2 0 0
The first few antidiagonals are:
1,
1, 2,
0, 1, 3,
1, 1, 2, 5,
0, 1, 0, 2, 7,
1, 1, 2, 2, 4, 11,
0, 1, 2, 0, 2, 2, 13,
1, 1, 2, 0, 0, 2, 4, 17,
0, 1, 2, 0, 0, 0, 2, 2, 19,
1, 1, 2, 0, 0, 0, 0, 2, 4, 23,
0, 1, 2, 0, 0, 0, 0, 0, 2, 6, 29,
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MATHEMATICA
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A362463[dmax_]:=With[{d=Reverse[NestList[Abs[Differences[#]]&, Join[{1}, Prime[Range[dmax-1]]], dmax-1]]}, Array[Diagonal[d, #]&, dmax, 1-dmax]]; A362463[20] (* Generates 20 antidiagonals *) (* Paolo Xausa, May 08 2023 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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