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

3,3

Links

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

Formula

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

Prog

(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

Crossrefs

Cf. A001917.

Sequence in context: A177196 A010741 A094643 * A327814 A188348 A336434

Adjacent sequences: A094590 A094591 A094592 * A094594 A094595 A094596

Keyword

nonn

Author

Benoit Cloitre, Jun 06 2004

Status

approved