A103497 - OEIS

%I #28 Mar 05 2023 12:40:20

%S 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,

%T 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,

%U 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

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

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

%C For n > 2, a(n) <= (n-1)/2. - _Robert Israel_, Mar 20 2020

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

%H Robert Israel, <a href="/A103497/b103497.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeOrder.html">Multiplicative Order</a>.

%H S. Wolfram, <a href="https://web.archive.org/web/20120925202826/http://www.stephenwolfram.com/publications/articles/ca/84-properties/9/text.html">Algebraic Properties of Cellular Automata (1984)</a>, Appendix B.

%p f:= proc(n) local x;

%p   if n mod 11 = 0 then return 0 fi;

%p   x:= numtheory:-mlog(-1,11,n);

%p   if x <> FAIL then x else numtheory:-order(11,n) fi

%p end proc:

%p f(1):= 0:

%p map(f, [$0..100]); # _Robert Israel_, Mar 20 2020

%t Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];

%t a[n_] := Suborder[11, n];

%t a /@ Range[0, 100] (* _Jean-François Alcover_, Mar 21 2020, after _T. D. Noe_ in A003558 *)

%K easy,nonn,look

%O 0,8

%A _Harry J. Smith_, Feb 08 2005