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 A001915 Primes p such that the congruence 2^x = 3 (mod p) is solvable. (Formerly M3807 N1555) 3
 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; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is known to be infinite [Polya] - thanks to Pieter Moree and Daniel Stefankovic for this comment, Dec 21 2009 REFERENCES M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 63. 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). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 G. Polya, Arithmetische Eigenschaften der Reihenentwicklungen rationaler Funktionen, J. reine und angewandte Mathematik (Crelle), Volume 1921, Issue 151, Pages 1-31. MAPLE N:= 1000: # to search the first N primes {2} union select(t -> numtheory[mlog](3, 2, p) <> FAIL, {seq(ithprime(n), n=2..N)}); # Robert Israel, Feb 15 2013 MATHEMATICA Select[Prime[Range[120]], MemberQ[Table[Mod[2^x-3, #], {x, 0, #}], 0]&] (* Jean-François Alcover, Aug 29 2011 *) PROG (PARI) isok(p) = isprime(p) && sum(k=0, (p-1), Mod(2, p)^k == 3); \\ Michel Marcus, Mar 12 2017 (PARI) is(n)=isprime(n) && (n==2 || #znlog(3, Mod(2, n))) \\ Charles R Greathouse IV, Aug 15 2018 CROSSREFS Cf. A001916. Sequence in context: A031869 A194854 A045360 * A127437 A084792 A109640 Adjacent sequences:  A001912 A001913 A001914 * A001916 A001917 A001918 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Better description from Joe K. Crump (joecr(AT)carolina.rr.com), Dec 11 2000 More terms from David W. Wilson, Dec 12 2000 STATUS approved

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Last modified December 9 20:24 EST 2018. Contains 318023 sequences. (Running on oeis4.)