

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
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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'x1, n)[, 1]); f=select(t>poldegree(t)==1, f); #f==1 && znorder(polcoeff(f[1], 0))==n1 \\ Charles R Greathouse IV, Nov 26 2014


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



