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A282063 A(n, k) = k-th Wilson prime p of order n with p >= n and k running over the positive integers. Square array read by antidiagonals.

%I A282063 #11 Feb 16 2025 08:33:40
%S A282063 5,13,2,563,3,7
%N A282063 A(n, k) = k-th Wilson prime p of order n with p >= n and k running over the positive integers. Square array read by antidiagonals.
%C A282063 A Wilson prime of order n is a prime p such that (n-1)!*(p-n)!-(-1)^n == 0 (modulo p^2).
%H A282063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WilsonPrime.html">Wilson Prime</a>
%H A282063 Wikipedia, <a href="http://en.wikipedia.org/wiki/Wilson_prime">Wilson prime</a>
%e A282063 Array A(n, k) starts:
%e A282063       5,   13,  563
%e A282063       2,    3,   11,  107, 4931
%e A282063       7
%e A282063   10429
%e A282063       5,    7,   47
%e A282063      11
%o A282063 (PARI) is_wilson(n, order) = Mod((order-1)!*(n-order)!-(-1)^order, n^2)==0
%o A282063 table(rows, cols) = for(x=1, rows, my(i=0); forprime(p=x, , if(is_wilson(p, x), print1(p, ", "); i++; if(i==cols, print(""); break))))
%o A282063 table(4, 3) \\ print initial 4 rows and 3 columns of table
%Y A282063 Cf. A007540 (row 1), A079853 (row 2), A152413 (row 17), A128666 (column 1).
%K A282063 nonn,hard,tabl,more
%O A282063 1,1
%A A282063 _Felix Fröhlich_, Feb 05 2017