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

Jianing Song, Table of n, a(n) for n = 1..1000

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), 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 A375921

Keyword

nonn

Author

Jianing Song, Sep 02 2024

Status

approved