A375916 Composite numbers k == 3, 7 (mod 10) such that 5^((k-1)/2) == -1 (mod k).

7813, 121463, 195313, 216457, 315283, 319507, 353827, 555397, 559903, 753667, 939727, 1164083, 1653667, 1663213, 1703677, 1809697, 1958503, 2255843, 2339377, 2423323, 2942333, 2987167, 3313643, 4265257, 4635053, 5376463, 5979247, 6611977, 7784297, 7859707

Offset: 1

Author

Jianing Song, Sep 02 2024

Keywords

• nonn

Comments

Odd composite numbers k such that 5^((k-1)/2) == (5/k) = -1 (mod k), where (5/k) is the Jacobi symbol (or Kronecker symbol).

Examples

			216457 is a term because 216457 = 233*929 is a composite, 216457 == 7 (mod 10), and 5^((216457-1)/2) == -1 (mod 216457).
		

Links

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

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 | A375918 | this seq |

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

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) | | | |

Programs

PARI

isA375916(k) = !isprime(k) && (k%10==3 || k%10==7) && Mod(5,k)^((k-1)/2) == -1