cp's OEIS Frontend

A317745 Square array T(n,k) (n >= 1, k >= 1) read by antidiagonals: first row and column are A085090, other entries equal sum of entries in first row and first column.

%I A317745 #72 Dec 05 2019 04:17:39
%S A317745 0,3,3,5,6,5,7,8,8,7,0,10,10,10,0,11,3,12,12,3,11,13,14,5,14,5,14,13,
%T A317745 0,16,16,7,7,16,16,0,17,3,18,18,0,18,18,3,17,19,20,5,20,11,11,20,5,20,
%U A317745 19,0,22,22,7,13,22,13,7,22,22,0,23,3,24,24,0,24,24,0,24,24,3,23
%N A317745 Square array T(n,k) (n >= 1, k >= 1) read by antidiagonals: first row and column are A085090, other entries equal sum of entries in first row and first column.
%C A317745 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 A317745 The successive antidiagonals may also be regarded as the rows of a triangle, having A085090 as outside diagonals.
%H A317745 Gustavo Funes, Damian Gulich, Leopoldo Garavaglia and Mario Garavaglia, <a href="http://www.mi.sanu.ac.rs/vismath/garavaglia2008/index.html">Hidden Symmetries Among Primes</a>, Form and Symmetry: Art and Science, Buenos Aires Congress, 2007, Section 4, Figure 10.
%H A317745 Fred Daniel Kline, <a href="/A317745/a317745_3.pdf">Goldbach Illustrated</a>
%F A317745 T(n, k) = A085090(n) + A085090(k).
%e A317745 Beginning of the array. All elements are equal to topmost value plus leftmost value.
%e A317745    0  3  5  7  0 11 13  0 17 19  0 23
%e A317745    3  6  8 10  3 14 16  3 20 22  3
%e A317745    5  8 10 12  5 16 18  5 22 24
%e A317745    7 10 12 14  7 18 20  7 24
%e A317745    0  3  5  7  0 11 13  0
%e A317745   11 14 16 18 11 22 24
%e A317745   13 16 18 20 13 24
%e A317745    0  3  5  7  0
%e A317745   17 20 22 24
%e A317745   19 22 24
%e A317745    0  3
%e A317745   23
%t A317745 i[n_] := If[PrimeQ[2 n - 1], 2 n - 1, 0]; A085090 = Array[i, 82];
%t A317745 r[k_] := Table[A085090[[j]] + A085090[[k - j + 1]], {j, 1, k}];
%t A317745 a = Array[r, 12] // Flatten,
%o A317745 (PARI) a085090(n) = if (isprime(p=2*n-1), p, 0);
%o A317745 row(n) = vector(n, k, a085090(k) + a085090(n-k+1));
%o A317745 tabl(nn) = for (n=1, nn, print(row(n))); \\ _Michel Marcus_, Aug 09 2018
%Y A317745 Cf. A085090.
%K A317745 nonn,tabl
%O A317745 1,2
%A A317745 _Fred Daniel Kline_, Aug 05 2018
%E A317745 Edited by _N. J. A. Sloane_, Sep 09 2018