

A058853


Primes p such that x^43 = 2 has a solution mod p.


6



2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
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OFFSET

1,1


COMMENTS

Primes not of the form 43n + 1.  Charles R Greathouse IV, Aug 22 2011
Differs from A000040  the prime 173 does not appear.
For case x^31 = 2 the first missing prime is 311 (64th term).
For case x^47 = 2 the first missing prime is 283 (61st term).
For case x^59 = 2 the first missing prime is 709 (127th term).
For case x^61 = 2 the first missing prime is 367 (73rd term).
Complement of A059243 relative to A000040.  Vincenzo Librandi, Sep 14 2012


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000
Index entries for related sequences


FORMULA

a(n) ~ 42/41 * n log n.  Charles R Greathouse IV, Aug 22 2011


MATHEMATICA

ok[p_]:= Reduce[Mod[x^43  2, p] == 0, x, Integers] =!= False; Select[Prime[Range[1000]], ok] (* Vincenzo Librandi Sep 14 2012 *)


PROG

(PARI) forprime(p=2, 1e3, if(p%43!=1, print1(p", "))) \\ Charles R Greathouse IV, Aug 22 2011
(MAGMA) [p: p in PrimesUpTo(400)  exists(t){x : x in ResidueClassRing(p)  x^43 eq 2}]; // Vincenzo Librandi Sep 14 2012


CROSSREFS

Sequence in context: A077359 A057448 A049551 * A049569 A100725 A050260
Adjacent sequences: A058850 A058851 A058852 * A058854 A058855 A058856


KEYWORD

nonn,easy


AUTHOR

Patrick De Geest, Dec 15 2000


STATUS

approved



