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A001915
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Primes p such that the congruence 2^x = 3 (mod p) is solvable.
(Formerly M3807 N1555)
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2
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2, 5, 11, 13, 19, 23, 29, 37, 47, 53, 59, 61, 67, 71, 83, 97, 101, 107, 131, 139, 149, 163, 167, 173, 179, 181, 191, 193, 197, 211, 227, 239, 263, 269, 293, 307, 311, 313, 317, 347, 349, 359, 373, 379, 383, 389, 409, 419, 421, 431, 443, 461, 467, 479, 491, 499, 503, 509, 523
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The sequence is known to be infinite [Polya] - thanks to Pieter Moree and Daniel Stefankovic for this comment, Dec 21 2009.
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REFERENCES
| M. Kraitchik, Recherches sur la Th\'{e}orie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 63.
G. Polya, Arithmetische Eigenschaften der Reihenentwicklungen rationaler Funktionen, J. reine und angewandte Mathematik (Crelle), Volume 1921, Issue 151, Pages 1-31.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
| Select[Prime[Range[120]], MemberQ[Table[Mod[2^x-3, #], {x, 0, #}], 0]&] (* From Jean-François Alcover, Aug 29 2011 *)
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CROSSREFS
| Cf. A001916.
Sequence in context: A031869 A194854 A045360 * A127437 A084792 A109640
Adjacent sequences: A001912 A001913 A001914 * A001916 A001917 A001918
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description from Joe K. Crump (joecr(AT)carolina.rr.com), Dec 11, 2000.
More terms from David W. Wilson (davidwwilson(AT)comcast.net), Dec 12 2000
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