login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059236 Primes p such that x^41 = 2 has no solution mod p. 19
83, 739, 821, 1231, 1559, 1723, 2297, 2543, 2707, 2789, 2953, 3527, 3691, 4019, 5003, 5167, 5413, 5659, 5741, 5987, 6151, 6397, 6971, 7873, 8447, 8693, 9103, 9349, 9431, 9677, 9923, 10169, 10333, 11071, 11317, 11399, 12301, 12547, 13121, 13367 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A049573 relative to A000040.

Presumably this is also "Primes congruent to 1 mod 41" (A212379), but that requires a proof. - N. J. A. Sloane, Jul 11 2008

Smallest counterexample: 17467 is not in A059236, but congruent to 1 mod 41 (17467 = 426*41+1). - Klaus Brockhaus, May 18 2011

LINKS

Klaus Brockhaus, Table of n, a(n) for n = 1..100000

MATHEMATICA

ok[p_]:= Reduce[Mod[x^41 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2000]], ok] (* Vincenzo Librandi, Sep 20 2012 *)

Select[Prime[Range[PrimePi[14000]]], ! MemberQ[PowerMod[Range[#], 41, #], Mod[2, #]] &] (* Bruno Berselli, Sep 20 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(13400) | not exists{x: x in ResidueClassRing(p) | x^41 eq 2}]; // Klaus Brockhaus, May 18 2011

(MAGMA) /* Alternatively: */ [p: p in PrimesUpTo(13400) | forall{x: x in ResidueClassRing(p) | x^41 ne 2}]; // Bruno Berselli, Sep 20 2012

(PARI) forprime(p=2, 69589957, if(trap(, 1, sqrtn(Mod(2, p), 41); 0), print1(p, ", "))) \\ Klaus Brockhaus, May 18 2011

(PARI)

N=10^5;  default(primelimit, N);

ok(p, r, k)={ return ( (p==r) || (Mod(r, p)^((p-1)/gcd(k, p-1))==1) ); }

forprime(p=2, N, if (! ok(p, 2, 41), print1(p, ", ")));

/* Joerg Arndt, Sep 21 2012 */

CROSSREFS

Subsequence of A212379.

Cf. A049573, A142199, A142200, A190758.

Sequence in context: A164758 A142751 A176633 * A212379 A059935 A069596

Adjacent sequences:  A059233 A059234 A059235 * A059237 A059238 A059239

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jan 20 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 2 18:43 EDT 2020. Contains 333189 sequences. (Running on oeis4.)