|
|
A089588
|
|
a(n) = A089587(2^n+1) for n >= 0.
|
|
1
|
|
|
1, 2, 2, 7, 2, 9, 38, 79, 2, 220, 821, 1780, 2168
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|