login
A103489
Multiplicative suborder of 3 (mod n) = sord(3, n).
0
0, 0, 1, 0, 1, 2, 0, 3, 2, 0, 2, 5, 0, 3, 3, 0, 4, 8, 0, 9, 4, 0, 5, 11, 0, 10, 3, 0, 3, 14, 0, 15, 8, 0, 8, 12, 0, 9, 9, 0, 4, 4, 0, 21, 10, 0, 11, 23, 0, 21, 10, 0, 6, 26, 0, 20, 6, 0, 14, 29, 0, 5, 15, 0, 16, 12, 0, 11, 16, 0, 12, 35, 0, 6, 9, 0, 9, 30, 0, 39, 4, 0, 4, 41, 0, 16, 21, 0, 10, 44
OFFSET
0,6
COMMENTS
a(n) is minimum e for which 3^e = +/-1 mod n, or zero if no e exists.
REFERENCES
H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3
LINKS
Eric Weisstein's World of Mathematics, Multiplicative Order.
Eric Weisstein's World of Mathematics, Suborder Function
MATHEMATICA
Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[3, n];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)
CROSSREFS
Sequence in context: A257541 A120854 A035159 * A213944 A127479 A284124
KEYWORD
easy,nonn
AUTHOR
Harry J. Smith, Feb 08 2005
STATUS
approved