The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 14 12:19 EDT 2024. Contains 373400 sequences. (Running on oeis4.)