|
|
A134572
|
|
Prime numbers p for which there is exactly one root x of x^3 - x - 1 in F_p and x is a primitive root mod p.
|
|
1
|
|
|
5, 7, 11, 17, 37, 67, 83, 113, 199, 227, 241, 251, 283, 367, 373, 401, 433, 457, 479, 569, 571, 613, 643, 659, 701, 727, 743, 757, 769, 839, 919, 941, 977, 1019, 1031, 1049, 1103, 1109, 1171, 1187, 1201, 1249, 1279, 1367, 1399, 1423, 1433, 1471, 1487, 1493, 1583, 1601
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Gil, Weiner, & Zara prove that there is a unique complete Padovan sequence in F_p for each prime p in this sequence, which is generated by x. - Charles R Greathouse IV, Nov 26 2014
|
|
LINKS
|
|
|
PROG
|
(PARI) is(n)=if(!isprime(n), return(0)); my(f=factormod('x^3-'x-1, n)[, 1]); f=select(t->poldegree(t)==1, f); #f==1 && znorder(-polcoeff(f[1], 0))==n-1 \\ Charles R Greathouse IV, Nov 26 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|