A053451 Multiplicative order of 8 mod 2n+1.

1, 2, 4, 1, 2, 10, 4, 4, 8, 6, 2, 11, 20, 6, 28, 5, 10, 4, 12, 4, 20, 14, 4, 23, 7, 8, 52, 20, 6, 58, 20, 2, 4, 22, 22, 35, 3, 20, 10, 13, 18, 82, 8, 28, 11, 4, 10, 12, 16, 10, 100, 17, 4, 106, 12, 12, 28, 44, 4, 8, 110, 20, 100, 7, 14, 130, 6, 12, 68, 46, 46, 20, 28, 14, 148, 5

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

In the case n=2 and any other case where a(n)=A000010(2n+1), the multiplicative group of units modulo 2n+1 is cyclic and thus 8 (and any other unit) is a generator. These moduli are A167796, so this occurs whenever 2n+1 (caution: not n) is a member of A167796. - Kellen Myers, Feb 06 2015

Examples

			The third term a(2) is 4 because 4 is the smallest integer such that 8^4 is congruent to 1 modulo 2*2+1=5. The orbit of 8 modulo 5 is {3, 4, 2, 1}. - _Kellen Myers_, Feb 06 2015
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Multiplicative Order

Crossrefs

Cf. A050980, A070667-A070675, A002326, A070676, A053447, A070677, A070681, A070678, A070679, A070682, A070680, A070683.

Programs

GAP

List([0..80],n->OrderMod(8,2*n+1)); # Muniru A Asiru, Feb 26 2019

Magma

[1] cat [Modorder(8, 2*n+1): n in [1..100]]; // Vincenzo Librandi, Apr 01 2014

Mathematica

Table[MultiplicativeOrder[8, n], {n, 1, 150, 2}] (* Robert G. Wilson v, Apr 05 2011 *)

PARI

vector(80, n, n--; znorder(Mod(8, 2*n+1))) \\ Michel Marcus, Feb 05 2015