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URL: https://oeis.org/A072190

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A072190
Indices of primes with primitive root 2.
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
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].
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
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