0,2

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.

a(2^k+1) = 2 for k>=0 (conjecture).

(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}

Cf. A089587, A000215.

Sequence in context: A138115 A021444 A029632 this_sequence A014840 A077218 A102780

Adjacent sequences: A089585 A089586 A089587 this_sequence A089589 A089590 A089591

more,nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 09 2003