A211173 (2n)!^n (modulo 2n+1).

0, 2, 1, 6, 0, 10, 1, 0, 1, 18, 0, 22, 0, 0, 1, 30, 0, 0, 1, 0, 1, 42, 0, 46, 0, 0, 1, 0, 0, 58, 1, 0, 0, 66, 0, 70, 1, 0, 0, 78, 0, 82, 0, 0, 1, 0, 0, 0, 1, 0, 1, 102, 0, 106, 1, 0, 1, 0, 0, 0, 0, 0, 0, 126, 0, 130, 0, 0, 1, 138, 0

Offset

0,2

Comments

a(n)= 0, 1 or 2n. In fact, a(n) = 0 iff n belongs to A047845, a(n) = 1 iff n belongs to A104636 and a(n) = 2n iff n belongs to A104635.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Larry Riddle, Sophie Germain and Fermat's Last Theorem, Agnes Scott College, Math. Dept. Jul, 1999.

Formula

a(n) = (2n)!^n (modulo 2n+1).

Mathematica

f[n_] := Mod[((2 n)!)^n, 2 n + 1]; Array[f, 70]
Table[PowerMod[(2n)!, n, 2n+1], {n, 0, 70}] (* Harvey P. Dale, Nov 02 2019 *)

Prog

(PARI) a(n)=if(isprime(2*n+1), if(n%2, 2*n, 1), 0) \\ Charles R Greathouse IV, Feb 07 2013

Crossrefs

Cf. A047845, A104635, A104636.

Sequence in context: A370901 A198812 A155183 * A163553 A078503 A288052

Adjacent sequences: A211170 A211171 A211172 * A211174 A211175 A211176

Keyword

nonn,easy

Author

Larry Riddle (LRiddle(AT)AgnesScott.edu) and Robert G. Wilson v, Jan 31 2013

Status

approved