A001915 Primes p such that the congruence 2^x == 3 (mod p) is solvable. (Formerly M3807 N1555)

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

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, A050259, A123988.

Sequence in context: A031869 A194854 A045360 * A127437 A339035 A084792

Adjacent sequences: A001912 A001913 A001914 * A001916 A001917 A001918

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

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