A007348 Primes for which -10 is a primitive root.

3, 17, 29, 31, 43, 61, 67, 71, 83, 97, 107, 109, 113, 149, 151, 163, 181, 191, 193, 199, 227, 229, 233, 257, 269, 283, 307, 311, 313, 337, 347, 359, 389, 431, 433, 439, 443, 461, 467, 479, 509, 523, 541, 563, 577, 587, 593, 599, 631, 683, 701, 709, 719, 787, 821, 827, 839

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Keywords

• nonn

Comments

Union of long period primes (A006883) of the form 4k+1 and half period primes (A097443) of the form 4k+3. - Davide Rotondo, Aug 25 2021

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), Table 24.8, p. 864.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• R. J. Mathar, Table of n, a(n) for n = 1..10000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Robert G. Wilson v, Letter to N. J. A. Sloane, Aug. 1993
• Index entries for primes by primitive root

Crossrefs

Cf. A038880.

Cf. A006883, A097443.

Programs

Mathematica

pr=-10; Select[Prime[Range[200 ] ], MultiplicativeOrder[pr, # ] == #-1 & ]

PARI

is(n)=gcd(n,10)==1 && znorder(Mod(-10,n))==n-1 \\ Charles R Greathouse IV, Nov 25 2014

Extensions

More terms from N. J. A. Sloane, Apr 24 2005

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

A&S reference and Mathematica program corrected by T. D. Noe, Nov 04 2009