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.

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

Author

Joseph Lewittes (jlewittes(AT)optonline.net), Nov 20 2003

Keywords

• nonn

Comments

For each 4k+1 prime, half of the permutations are even, half are odd.

Examples

			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

Cf. A002144, A002145.

Extensions

Edited by Don Reble, Jul 31 2006