A003573 Order of 4 mod 4n+1.

1, 2, 3, 6, 4, 3, 10, 14, 5, 18, 10, 6, 21, 26, 9, 30, 6, 11, 9, 15, 27, 4, 11, 5, 24, 50, 6, 18, 14, 6, 55, 50, 7, 9, 34, 23, 14, 74, 12, 26, 33, 10, 78, 86, 29, 90, 18, 9, 48, 98, 33, 10, 45, 35, 15, 12, 30, 38, 29, 39, 12, 42, 41, 55, 8, 42, 26, 134, 6, 46, 35

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003574. First bisection of A053447.

Cf. A002326, A003571, A217469.

Programs

GAP

List([0..70],n->OrderMod(4,4*n+1)); # Muniru A Asiru, Feb 16 2019

Maple

a := n -> `if`(n=0, 1, numtheory:-order(4, 4*n+1)): seq(a(n), n = 0..68);

Mathematica

Table[MultiplicativeOrder[4, 4*n + 1], {n, 0, 70}] (* Arkadiusz Wesolowski, Nov 27 2012 *)

PARI

a(n) = znorder(Mod(4, 4*n+1)); \\ Michel Marcus, Feb 16 2019

Sage

def A003573(n):
    s, m, N = 0, 1, 4*n + 1
    while True:
        k = N + m
        v = valuation(k, 4)
        s += v
        m = k // 4^v
        if m == 1: break
    return s
print([A003573(n) for n in (0..70)]) # Peter Luschny, Oct 07 2017

Formula

a(n) = A053447(2*n) for n >= 0. - Jianing Song, Oct 03 2022

Extensions

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