|
Search: id:A088592
|
|
|
| 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
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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
|
Cf. A002144, A002145.
Sequence in context: A120528 A074201 A068433 this_sequence A029692 A071906 A104107
Adjacent sequences: A088589 A088590 A088591 this_sequence A088593 A088594 A088595
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joseph Lewittes (jlewittes(AT)optonline.net), Nov 20 2003
|
|
EXTENSIONS
|
Edited by Don Reble (djr(AT)nk.ca), Jul 31 2006
|
|
|
Search completed in 0.002 seconds
|
