This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A323377 #27 Jan 20 2019 09:45:06 %S A323377 0,-1,-1,-1,0,-1,1,-1,-1,1,-1,1,0,-1,-1,-1,-1,-1,-1,1,-1,1,1,1,0,1,1, %T A323377 1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,-1,0,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1, %U A323377 1,1,-1,1,-1,-1,-1,-1,0,-1,1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1 %N A323377 Square array read by ascending antidiagonals: T(n,k) = Kronecker(prime(n)/prime(k)), n, k >= 1. %C A323377 The n-th row is the same as the n-th column if and only if n = 1 or prime(n) == 1 (mod 4). %C A323377 In general, for any m != 0 and n > 0, Kronecker symbol (m/n) can be written as the product of the terms of this table and the terms of the form (-1/p) where p is any prime. %C A323377 According to Chebyshev's bias, there seem to be more -1's than 1's among the first terms of any row or any column. One can see from the table in the example section that there are 54 -1's and 36 1's in the upper left 10 X 10 square of the table. There are 5158 -1's and 4742 1's in the upper left 100 X 100 square of the table. %H A323377 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev%27s_bias">Chebyshev's bias</a> %F A323377 T(n,k) = A215200(prime(n) + prime(k), prime(k)). %e A323377 Table begins %e A323377 | k | 1 2 3 4 5 6 7 8 9 10 ... %e A323377 n | p() | 2 3 5 7 11 13 17 19 23 29 ... %e A323377 ---+-----+-------------------------------------------- %e A323377 1 | 2 | 0, -1, -1, 1, -1, -1, 1, -1, 1, -1, ... %e A323377 2 | 3 | -1, 0, -1, -1, 1, 1, -1, -1, 1, -1, ... %e A323377 3 | 5 | -1, -1, 0, -1, 1, -1, -1, 1, -1, 1, ... %e A323377 4 | 7 | 1, 1, -1, 0, -1, -1, -1, 1, -1, 1, ... %e A323377 5 | 11 | -1, -1, 1, 1, 0, -1, -1, 1, -1, -1, ... %e A323377 6 | 13 | -1, 1, -1, -1, -1, 0, 1, -1, 1, 1, ... %e A323377 7 | 17 | 1, -1, -1, -1, -1, 1, 0, 1, -1, -1, ... %e A323377 8 | 19 | -1, 1, 1, -1, -1, -1, 1, 0, -1, -1, ... %e A323377 9 | 23 | 1, -1, -1, 1, 1, 1, -1, 1, 0, 1, ... %e A323377 10 | 29 | -1, -1, 1, 1, -1, 1, -1, -1, 1, 0, ... %e A323377 ... %o A323377 (PARI) T(n,k) = kronecker(prime(n), prime(k)) %Y A323377 Cf. A215200. %Y A323377 Cf. A226523 (1st row and 1st column), A257834 (2nd row), A134323 (2nd column). %K A323377 sign,tabl %O A323377 1,1 %A A323377 _Jianing Song_, Jan 12 2019