cp's OEIS Frontend

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.

%I A088592 #3 Oct 19 2017 03:14:24
%S A088592 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,
%T A088592 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,
%U A088592 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
%N 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.
%C A088592 For each 4k+1 prime, half of the permutations are even, half are odd.
%e A088592 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).
%e A088592 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).
%Y A088592 Cf. A002144, A002145.
%K A088592 nonn
%O A088592 1,1
%A A088592 Joseph Lewittes (jlewittes(AT)optonline.net), Nov 20 2003
%E A088592 Edited by _Don Reble_, Jul 31 2006