A089588 a(n) = A089587(2^n+1) for n >= 0.

1, 2, 2, 7, 2, 9, 38, 79, 2, 220, 821, 1780, 2168

Offset

0,2

Comments

A089587(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 A089587(n)=2 only when n is a Fermat number 2^(2^j) + 1 for j >= 0.

Links

Table of n, a(n) for n=0..12.

Formula

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

Prog

(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}

Crossrefs

Cf. A089587, A000215.

Sequence in context: A138115 A021444 A029632 * A325211 A211780 A014840

Adjacent sequences: A089585 A089586 A089587 * A089589 A089590 A089591

Keyword

nonn,hard,more

Author

Paul D. Hanna, Nov 09 2003

Extensions

Definition corrected by Max Alekseyev, Sep 05 2023

Status

approved