A282063 - OEIS

%I #10 Mar 10 2017 06:58:49

%S 5,13,2,563,3,7

%N 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 A Wilson prime of order n is a prime p such that (n-1)!*(p-n)!-(-1)^n == 0 (modulo p^2).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WilsonPrime.html">Wilson Prime</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Wilson_prime">Wilson prime</a>

%e Array A(n, k) starts:

%e       5,   13,  563

%e       2,    3,   11,  107, 4931

%e       7

%e   10429

%e       5,    7,   47

%e      11

%o (PARI) is_wilson(n, order) = Mod((order-1)!*(n-order)!-(-1)^order, n^2)==0

%o 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 table(4, 3) \\ print initial 4 rows and 3 columns of table

%Y Cf. A007540 (row 1), A079853 (row 2), A152413 (row 17), A128666 (column 1).

%K nonn,hard,tabl,more

%O 1,1

%A _Felix Fröhlich_, Feb 05 2017