A007349 Primes with both 10 and -10 as primitive root.

17, 29, 61, 97, 109, 113, 149, 181, 193, 229, 233, 257, 269, 313, 337, 389, 433, 461, 509, 541, 577, 593, 701, 709, 821, 857, 937, 941, 953, 977, 1021, 1033, 1069, 1097, 1109, 1153, 1181, 1193, 1217, 1229, 1297, 1301, 1381, 1429, 1433, 1549, 1553, 1621, 1697, 1709, 1741, 1777, 1789, 1861, 1873, 1913, 1949

Offset: 1

Author

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

Keywords

• nonn

Comments

Intersection of A006883 and A002144. - Davide Rotondo, May 21 2025

References

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

Links

• 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. A002144, A006883.

Programs

Mathematica

pr=10; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == MultiplicativeOrder[-pr, # ] == #-1 &]
Select[Prime[Range[5,200]],PrimitiveRoot[#,10]==10&&PrimitiveRoot[#,#-10] == #-10&] (* Harvey P. Dale, Oct 10 2019 *)

PARI

forprime(p=11,2000,if(znorder(Mod(10,p))==p-1&&znorder(Mod(-10,p))==p-1,print1(p,", "))); \\ Joerg Arndt, May 21 2025