A317745 -id:A317745 - cp's OEIS frontend

A327910 This is the reduced A317745, with primes -> 1 and prime + prime -> 2.

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

Offset: 1

Fred Daniel Kline, Oct 05 2019

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.

			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.

Cf. A101264, A317745.

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,

T(n, k) = A101264(n) + A101264(k).

cp's OEIS Frontend

A327910 This is the reduced A317745, with primes -> 1 and prime + prime -> 2.

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