cp's OEIS Frontend

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

%I A327910 #9 Oct 16 2019 13:28:03
%S A327910 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,
%T A327910 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,
%U A327910 2,2,0,2,2,0,2,2,1,1
%N A327910 This is the reduced A317745, with primes -> 1 and prime + prime -> 2.
%C A327910 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.
%C A327910 The successive antidiagonals may also be regarded as the rows of a triangle, having A101264 as outside diagonals.
%F A327910 T(n, k) = A101264(n) + A101264(k).
%e A327910 Beginning of the array. All elements are equal to topmost value plus leftmost value.
%e A327910    0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2 1 2 2
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2 1 2
%e A327910    0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 2
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1
%e A327910    0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1 1 2 2
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1 1 2
%e A327910    0 1 1 1 0 1 1 0 1 1 0 1 0 0
%e A327910    1 2 2 2 1 2 2 1 2 2 1 2 1
%e A327910    0 1 1 1 0 1 1 0 1 1 0 1
%e A327910    0 1 1 1 0 1 1 0 1 1 0
%e A327910    1 2 2 2 1 2 2 1 2 2
%e A327910    1 2 2 2 1 2 2 1 2
%e A327910    0 1 1 1 0 1 1 0
%e A327910    0 1 1 1 0 1 1
%e A327910    1 2 2 2 1 2
%e A327910    0 1 1 1 0
%e A327910    1 2 2 2
%e A327910    1 2 2
%e A327910    0 1
%e A327910    1
%e A327910 Note: A101264 is both outside diagonals. A101264 and A101264 + 1 are inside diagonals, determined by their positions in the outside diagonals.
%t A327910 i[n_] := If[PrimeQ[2 n - 1], 2 n - 1, 0]; A101264 = Array[i, 82];
%t A327910 r[k_] := Table[A101264[[j]] + A101264[[k - j + 1]], {j, 1, k}];
%t A327910 a = Array[r, 12] // Flatten,
%Y A327910 Cf. A101264, A317745.
%K A327910 nonn,tabl
%O A327910 1,5
%A A327910 _Fred Daniel Kline_, Oct 05 2019