A003571 Order of 3 mod 3n+1.

1, 2, 6, 4, 3, 4, 18, 5, 20, 6, 30, 16, 18, 4, 42, 11, 42, 6, 20, 28, 10, 16, 22, 12, 12, 18, 78, 8, 16, 10, 6, 23, 48, 20, 34, 52, 27, 12, 44, 29, 5, 30, 126, 12, 18, 16, 138, 35, 28, 18, 50, 30, 78, 8, 162, 41, 39, 42, 60, 88, 45, 22, 80, 36, 16, 42, 198, 100, 8

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A002326, A003573, A217469.

Programs

GAP

List([0..70],n->OrderMod(3,3*n+1)); # Muniru A Asiru, Feb 16 2019

Maple

a := n -> `if`(n=0, 1, numtheory:-order(3, 3*n+1)):
seq(a(n), n = 0..68);

Mathematica

Table[MultiplicativeOrder[3, 3*n + 1], {n, 0, 68}] (* Arkadiusz Wesolowski, Nov 27 2012 *)

PARI

a(n) = znorder(Mod(3, 3*n+1)); \\ Michel Marcus, Feb 16 2019

Sage

def A003571(n):
    s, m, N = 0, 1, 3*n + 1
    while True:
        k = N + m
        v = valuation(k, 3)
        s += v
        m = k // 3^v
        if m == 1: break
    return s
print([A003571(n) for n in (0..68)]) # Peter Luschny, Oct 07 2017

Extensions

a(0) = 1 added by Peter Luschny, Oct 07 2017