A094593 a(n) = (p-1)/x, where p = prime(n) and x = ord(3,p), the smallest positive integer such that 3^x == 1 mod p.

1, 1, 2, 4, 1, 1, 2, 1, 1, 2, 5, 1, 2, 1, 2, 6, 3, 2, 6, 1, 2, 1, 2, 1, 3, 2, 4, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 2, 4, 2, 12, 1, 1, 1, 1, 2, 4, 1, 2, 2, 2, 1, 2, 1, 9, 4, 1, 1, 1, 9, 2, 8, 1, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 2, 4, 10, 16, 3, 2, 1, 2

Offset: 3

Author

Benoit Cloitre, Jun 06 2004

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A001917.

Programs

PARI

a(n)=(prime(n)-1)/if(n<0,0,k=1;while((3^k-1)%prime(n)>0,k++);k)

Python

from sympy import prime, n_order
def A094593(n):
    p = prime(n)
    return 1 if n == 3 else (p-1)//n_order(3,p) # Chai Wah Wu, Jan 15 2020

Formula

a(n) = (A000040(n)-1)/A062117(n).