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A327910
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This is the reduced A317745, with primes -> 1 and prime + prime -> 2.
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0
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0, 1, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 0, 2, 2, 1, 1, 2, 2, 0, 1, 1, 2, 2, 0, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 0, 2, 2, 1, 1, 2, 1, 1, 2, 2, 0, 1, 1, 2, 2, 0, 2, 2, 0, 2, 2, 1, 1
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OFFSET
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1,5
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COMMENTS
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This is related to Goldbach's conjecture, since entries for which the leftmost entry and the top entry are both nonzero are the sums of two primes.
The successive antidiagonals may also be regarded as the rows of a triangle, having A101264 as outside diagonals.
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LINKS
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Table of n, a(n) for n=1..78.
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FORMULA
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T(n, k) = A101264(n) + A101264(k).
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EXAMPLE
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Beginning of the array. All elements are equal to topmost value plus leftmost value.
0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1
1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2 1 2 2
1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2 1 2
0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0
1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2
1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1
0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0
1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2
1 2 2 2 1 2 2 1 2 2 1 2 1 1 2
0 1 1 1 0 1 1 0 1 1 0 1 0 0
1 2 2 2 1 2 2 1 2 2 1 2 1
0 1 1 1 0 1 1 0 1 1 0 1
0 1 1 1 0 1 1 0 1 1 0
1 2 2 2 1 2 2 1 2 2
1 2 2 2 1 2 2 1 2
0 1 1 1 0 1 1 0
0 1 1 1 0 1 1
1 2 2 2 1 2
0 1 1 1 0
1 2 2 2
1 2 2
0 1
1
Note: A101264 is both outside diagonals. A101264 and A101264 + 1 are inside diagonals, determined by their positions in the outside diagonals.
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MATHEMATICA
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i[n_] := If[PrimeQ[2 n - 1], 2 n - 1, 0]; A101264 = Array[i, 82];
r[k_] := Table[A101264[[j]] + A101264[[k - j + 1]], {j, 1, k}];
a = Array[r, 12] // Flatten,
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CROSSREFS
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Cf. A101264, A317745.
Sequence in context: A307777 A284593 A190672 * A242998 A140885 A064286
Adjacent sequences: A327907 A327908 A327909 * A327911 A327912 A327913
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KEYWORD
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nonn,tabl
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AUTHOR
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Fred Daniel Kline, Oct 05 2019
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STATUS
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approved
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