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.

5, 13, 2, 563, 3, 7

Offset: 1

Author

Felix Fröhlich, Feb 05 2017

Keywords

• nonn
• hard
• tabl
• more

Comments

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

Examples

			Array A(n, k) starts:
      5,   13,  563
      2,    3,   11,  107, 4931
      7
  10429
      5,    7,   47
     11
		

Links

• Eric Weisstein's World of Mathematics, Wilson Prime
• Wikipedia, Wilson prime

Crossrefs

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

Programs

PARI

is_wilson(n, order) = Mod((order-1)!*(n-order)!-(-1)^order, n^2)==0
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))))
table(4, 3) \\ print initial 4 rows and 3 columns of table