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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. 0
5, 13, 2, 563, 3, 7 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 16:32 EST 2023. Contains 359945 sequences. (Running on oeis4.)