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

1,1

Comments

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

Links

Table of n, a(n) for n=1..6.

Eric Weisstein's World of Mathematics, Wilson Prime

Wikipedia, Wilson prime

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A073878 A164793 A065934 * A035412 A338985 A065865

Adjacent sequences: A282060 A282061 A282062 * A282064 A282065 A282066

Keyword

nonn,hard,tabl,more

Author

Felix Fröhlich, Feb 05 2017

Status

approved