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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..102.

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

Cf. A002144, A002145.

Sequence in context: A164950 A068433 A266895 * A188189 A029692 A309849

Adjacent sequences:  A088589 A088590 A088591 * A088593 A088594 A088595

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Edited by Don Reble, Jul 31 2006

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)