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

1,1

Comments

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

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

Example

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.

Mathematica

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

Crossrefs

Cf. A001122, A001123, A001124, A001125.

Sequence in context: A249013 A211964 A140199 * A363658 A356137 A177445

Adjacent sequences: A072187 A072188 A072189 * A072191 A072192 A072193

Keyword

easy,nonn

Author

Miklos Kristof, Jul 02 2002

Extensions

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

Extended by T. D. Noe, Apr 16 2014

Status

approved