A120372 a(n) = ((2n)!+1)*((2n+2)!+1) mod (2n+1)*(2n+3).

0, 0, 28, 55, 0, 91, 136, 0, 190, 253, 276, 1, 406, 0, 496, 1, 666, 703, 820, 0, 946, 1081, 1128, 1, 1378, 1431, 1, 1711, 0, 1891, 1, 2211, 2278, 2485, 0, 2701, 1, 3081, 3160, 3403, 3486, 1, 3916, 4005, 1, 1, 4656, 4753, 5050, 0

Offset

1,3

Comments

a(n) = 0 iff 2n+1 is prime and 2n+3 is prime; a(n) = (n+1)*(2n+1) iff 2n+1 is prime and 2n+3 is composite; a(n) = (n+1)*(2n+3) iff 2n+1 is composite and 2n+3 is prime; a(n) = 1 iff 2n+1 is composite and 2n+3 is composite.

Links

Table of n, a(n) for n=1..50.

Example

a(2) = (4!+1)*(6!+1) mod (5*7) = 18025 mod 35 = 0, thus 2*2+1 = 5 and 2*2+3 = 7 are primes.

Mathematica

Table[Mod[((2n)! + 1)*((2n + 2)! + 1), (2n + 1)*(2n + 3)], {n, 1, 50}] (* Stefan Steinerberger, Jul 22 2006 *)

Crossrefs

Sequence in context: A044080 A044461 A056028 * A274642 A068129 A079731

Adjacent sequences: A120369 A120370 A120371 * A120373 A120374 A120375

Keyword

nonn

Author

Franz Vrabec, Jun 27 2006

Extensions

More terms from Stefan Steinerberger, Jul 22 2006

Status

approved