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A040034 Primes p such that x^3 = 2 has no solution mod p. 4
7, 13, 19, 37, 61, 67, 73, 79, 97, 103, 139, 151, 163, 181, 193, 199, 211, 241, 271, 313, 331, 337, 349, 367, 373, 379, 409, 421, 463, 487, 523, 541, 547, 571, 577, 607, 613, 619, 631, 661, 673, 709, 751, 757, 769, 787, 823, 829, 853, 859, 877, 883, 907, 937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes represented by the quadratic form 4x^2 + 2xy + 7y^2, whose discriminant is -108. - T. D. Noe, May 17 2005

Complement of A040028 relative to A000040. - Vincenzo Librandi, Sep 17 2012

LINKS

Klaus Brockhaus, Table of n, a(n) for n=1..1000

Steven R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251), 2007.

EXAMPLE

A cube modulo 7 can only be 0, 1 or 6, but not 2, hence the prime 7 is in the sequence.

Because x^3 = 2 mod 11 when x = 7 mod 11, the prime 11 is not in the sequence.

MATHEMATICA

insolublePrimeQ[p_]:= Reduce[Mod[x^3 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], insolublePrimeQ] (* Vincenzo Librandi Sep 17 2012 *)

PROG

(MAGMA) [ p: p in PrimesUpTo(937) | forall(t){x : x in ResidueClassRing(p) | x^3 ne 2} ]; // Klaus Brockhaus, Dec 05 2008

(PARI) forprime(p=2, 10^3, if(#polrootsmod(x^3-2, p)==0, print1(p, ", "))) \\ Joerg Arndt, Jul 16 2015

CROSSREFS

Sequence in context: A059262 A059640 A059643 * A176229 A266268 A110074

Adjacent sequences:  A040031 A040032 A040033 * A040035 A040036 A040037

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Klaus Brockhaus, Dec 05 2008

STATUS

approved

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Last modified June 16 21:20 EDT 2019. Contains 324155 sequences. (Running on oeis4.)