A062117 Order of 3 mod n-th prime.

1, 0, 4, 6, 5, 3, 16, 18, 11, 28, 30, 18, 8, 42, 23, 52, 29, 10, 22, 35, 12, 78, 41, 88, 48, 100, 34, 53, 27, 112, 126, 65, 136, 138, 148, 50, 78, 162, 83, 172, 89, 45, 95, 16, 196, 198, 210, 222, 113, 57, 232, 119, 120, 125, 256, 131, 268, 30, 69, 280, 282, 292, 34

Offset: 1

Author

Olivier Gérard, Jun 06 2001

Keywords

• easy
• nonn

Examples

			The 3rd prime is 5 and mod 5, 3^4 = 1, so a(3) = 4.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A019334 (full reptend primes in base 3).

In other bases: A014664, A082654, A211241, A211242, A211243, A211244, A211245, A002371.

Programs

GAP

A000040:=Filtered([1..350],IsPrime);;
List([1..Length(A000040)],n->OrderMod(3,A000040[n])); # Muniru A Asiru, Feb 07 2019

Mathematica

Table[With[{p=Prime[n]},If[p==3,0,MultiplicativeOrder[3,p]]],{n,63}] (* Ray Chandler, Apr 06 2016 *)

PARI

a(n,{base=3}) = my(p=prime(n)); if(base%p, znorder(Mod(base,p)), 0) \\ Jianing Song, May 13 2024

Python

from sympy import n_order, prime
def A062117(n): return n_order(3,prime(n)) if n != 2 else 0 # Chai Wah Wu, Nov 10 2023