A375918 Composite numbers k == 5, 7 (mod 12) such that 3^((k-1)/2) == -1 (mod k).

703, 1891, 3281, 8911, 12403, 16531, 44287, 63139, 79003, 97567, 105163, 152551, 182527, 188191, 211411, 218791, 288163, 313447, 320167, 364231, 385003, 432821, 453259, 497503, 563347, 638731, 655051, 658711, 801139, 859951, 867043, 973241, 994507, 1024651, 1097227

Offset

1,1

Comments

Odd composite numbers k such that 3^((k-1)/2) == (3/k) = -1 (mod k), where (3/k) is the Jacobi symbol (or Kronecker symbol).

Links

Table of n, a(n) for n=1..35.

Example

3281 is a term because 3281 = 17*193 is composite, 3281 == 5 (mod 12), and 3^((3281-1)/2) == -1 (mod 3281).

Prog

(PARI) isA375918(k) = !isprime(k) && (k%12==5 || k%12==7) && Mod(3, k)^((k-1)/2) == -1

Crossrefs

| b=2 | b=3 | b=5 |

-----------------------------------+-------------------+----------+---------+

(b/k)=1, b^((k-1)/2)==1 (mod k) | A006971 | A375917 | A375915 |

-----------------------------------+-------------------+----------+---------+

(b/k)=-1, b^((k-1)/2)==-1 (mod k) | A244628 U A244626 | this seq | A375916 |

-----------------------------------+-------------------+----------+---------+

b^((k-1)/2)==-(b/k) (mod k), | | | |

conjectured to be also | A306310 | A375490 | A375816 |

(b/k)=-1, b^((k-1)/2)==1 (mod k) | | | |

-----------------------------------+-------------------+----------+---------+

Euler-Jacobi pseudoprimes | A047713 | A048950 | A375914 |

(union of first two) | | | |

-----------------------------------+-------------------+----------+---------+

Euler pseudoprimes | A006970 | A262051 | A262052 |

(union of all three) | | | |

Sequence in context: A214486 A045146 A083735 * A161021 A283521 A334010

Adjacent sequences: A375915 A375916 A375917 * A375919 A375920 A375924

Keyword

nonn,new

Author

Jianing Song, Sep 02 2024

Status

approved