%I A089588
%S A089588 1,2,2,7,2,9,38,79,2,220,821,1780,2168
%N A089588 a(n)=A089588(2^n+1) for n>=0.
%C A089588 A089588(n) is the smallest integer k, 0<k<n, that most often satisfies 
               the condition: k^m > k^(m+1) (modulo n) as m varies from 1 to n-1, 
               for n>2, with a(1)=0 and a(2)=1. It is conjectured that A089588(n)=2 
               only when n is a Fermat number 2^(2^j)+1 for j>=0.
%F A089588 a(2^k+1) = 2 for k>=0 (conjecture).
%o A089588 (PARI) {a(n)=local(A); n>=0; M=0; A=1; for(k=1,2^n,S=sum(j=1,2^n,if(k^j%(2^n+1)>
               k^(j+1)%(2^n+1),1,0)); if(S>M,M=S; A=k)); A}
%Y A089588 Cf. A089587, A000215.
%Y A089588 Sequence in context: A138115 A021444 A029632 this_sequence A014840 A077218 
               A102780
%Y A089588 Adjacent sequences: A089585 A089586 A089587 this_sequence A089589 A089590 
               A089591
%K A089588 more,nonn
%O A089588 0,2
%A A089588 Paul D. Hanna (pauldhanna(AT)juno.com), Nov 09 2003