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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
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
Juan B. Gil, Michael D. Weiner and Catalin Zara, Complete Padovan sequences in finite fields, The Fibonacci Quarterly, Volume 45 Number 1, Feb 2007, pp. 64-75, see p. 71.
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
Cf. A134573.
Sequence in context: A046140 A023241 A174357 * A106954 A027755 A260828
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Nov 01 2007
EXTENSIONS
Corrected and extended by Charles R Greathouse IV, Nov 26 2014
New name from Charles R Greathouse IV, Nov 26 2014
STATUS
approved