A072190 Indices of primes with primitive root 2.

2, 3, 5, 6, 8, 10, 12, 16, 17, 18, 19, 23, 26, 28, 32, 34, 35, 38, 40, 41, 42, 45, 47, 49, 57, 62, 66, 69, 70, 74, 75, 77, 81, 82, 86, 89, 91, 94, 97, 99, 100, 101, 102, 103, 107, 112, 114, 119, 120, 121, 123, 126, 127, 134, 137, 138, 139, 142, 144, 145, 147

Offset: 1

Author

Miklos Kristof, Jul 02 2002

Keywords

• easy
• nonn

Comments

Artin conjectured that this sequence is infinite (this is the famous Artin Conjecture).

Examples

			8 is an element of the sequence: 19 the 8th prime and 2 is primitive root of 19. 9 is not element of the sequence, since 23 is the 9th prime and 2 is not primitive root of 23.
		

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
• J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, New York, 1996. see p. 169
• L. Huber, manuscripts on Group Theory and Number Theory, 1990-1995

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• 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].
• Index entries for sequences related to Artin's conjecture

Crossrefs

Cf. A001122, A001123, A001124, A001125.

Programs

Mathematica

Select[Range[300], MultiplicativeOrder[2, Prime[#]] == Prime[#] - 1 &] (* T. D. Noe, Apr 16 2014 *)

Extensions

Edited by N. J. A. Sloane, Apr 11 2009

Extended by T. D. Noe, Apr 16 2014