A049563 a(n) = ((prime(n)-1)! + 1) mod (prime(n) + 2).

2, 3, 4, 1, 7, 1, 10, 1, 1, 16, 1, 1, 22, 1, 1, 1, 31, 1, 1, 37, 1, 1, 1, 1, 1, 52, 1, 55, 1, 1, 1, 1, 70, 1, 76, 1, 1, 1, 1, 1, 91, 1, 97, 1, 100, 1, 1, 1, 115, 1, 1, 121, 1, 1, 1, 1, 136, 1, 1, 142, 1, 1, 1, 157, 1, 1, 1, 1, 175, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 211, 1, 217, 1, 1, 1, 1, 1

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

Residue of (prime(n)-1)!+1 modulo prime(n)+2.

Examples

			a(3) = 4 since prime(3) = 5, and 4! + 1 = 25 gives residue 4 when divided by prime(3) + 2 = 7.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052147, A060371.

Programs

Magma

[(Factorial(p-1)+1) mod (p+2): p in PrimesUpTo(500)]; // Bruno Berselli, Apr 10 2015

Mathematica

Table[Mod[(Prime[k] - 1)! + 1, Prime[k] + 2], {k, 1, 200}]

PARI

a(n) = ((prime(n)-1)! + 1) % (prime(n) + 2); \\ Michel Marcus, May 28 2018

Sage

[Mod(factorial(p-1)+1,p+2) for p in primes(500)] # Bruno Berselli, Apr 10 2015

Formula

a(n) = A060371(n) mod A052147(n). - Amiram Eldar, Mar 13 2025