login
A088592
Let p be the n-th 4k+3 prime (A002145), g be any primitive root of p. The mapping x->g^x mod p gives a permutation of {1,2,...,p-1}. a(n) is 0 if the permutation is even for each g, 1 if odd for each g.
0
1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1
OFFSET
1,1
COMMENTS
For each 4k+1 prime, half of the permutations are even, half are odd.
EXAMPLE
a(2)=0 because x->g^x mod 7 gives an even permutation for each primitive root of 7. For p.r.=3, the cycles are (1 3 6)(2)(4)(5).
a(5)=1 because x->g^x mod 23 gives an odd permutation for each primitive root of 23. For p.r.=5, the cycles are (1 5 20 12 18 6 8 16 3 10 9 11 22)(2)(4)(7 17 15 19)(13 21 14).
CROSSREFS
Sequence in context: A164950 A068433 A266895 * A188189 A029692 A309849
KEYWORD
nonn
AUTHOR
Joseph Lewittes (jlewittes(AT)optonline.net), Nov 20 2003
EXTENSIONS
Edited by Don Reble, Jul 31 2006
STATUS
approved