A103497 Multiplicative suborder of 11 (mod n) = sord(11, n).

0, 0, 1, 1, 1, 1, 1, 3, 2, 3, 1, 0, 1, 6, 3, 2, 4, 8, 3, 3, 2, 6, 0, 11, 2, 5, 6, 9, 6, 14, 2, 15, 8, 0, 8, 3, 3, 3, 3, 12, 2, 20, 6, 7, 0, 6, 11, 23, 4, 21, 5, 16, 12, 13, 9, 0, 6, 6, 14, 29, 2, 2, 15, 6, 16, 12, 0, 33, 16, 11, 3, 35, 6, 36, 3, 10, 6, 0, 12, 39, 4, 27, 20, 41, 6, 16, 7, 28, 0, 11, 6

Offset

0,8

Comments

a(n) is minimum e for which 11^e == +-1 (mod n), or zero if no such e exists.

For n > 2, a(n) <= (n-1)/2. - Robert Israel, Mar 20 2020

References

H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Multiplicative Order.

S. Wolfram, Algebraic Properties of Cellular Automata (1984), Appendix B.

Maple

f:= proc(n) local x;
  if n mod 11 = 0 then return 0 fi;
  x:= numtheory:-mlog(-1, 11, n);
  if x <> FAIL then x else numtheory:-order(11, n) fi
end proc:
f(1):= 0:
map(f, [$0..100]); # Robert Israel, Mar 20 2020

Mathematica

Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[11, n];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)

Crossrefs

Sequence in context: A048967 A324182 A166592 * A191390 A309698 A369997

Adjacent sequences: A103494 A103495 A103496 * A103498 A103499 A103500

Keyword

easy,nonn,look

Author

Harry J. Smith, Feb 08 2005

Status

approved