A375914 Base-5 Euler-Jacobi pseudoprimes: odd composite k coprime to 5 such that 5^((k-1)/2) == (5/k) (mod n), where (5/k) is the Jacobi symbol (or Kronecker symbol).

781, 1541, 1729, 5461, 5611, 6601, 7449, 7813, 11041, 12801, 13021, 14981, 15751, 15841, 21361, 24211, 25351, 29539, 38081, 40501, 41041, 44801, 47641, 53971, 67921, 75361, 79381, 90241, 100651, 102311, 104721, 106201, 106561, 112141, 113201, 115921, 121463, 133141

Offset: 1

Author

Jianing Song, Sep 02 2024

Keywords

• nonn

Examples

			781 is a term because 781 = 11*71 is composite, (5/781) = 1, and 5^((781-1)/2) == 1 (mod 781).
7813 is a term because 7813 = 13*601 is composite, (5/7813) = -1, and 5^((7813-1)/2) == -1 (mod 7813).
		

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 | 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 | this seq |

(union of first two) | | | |

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

Euler pseudoprimes | A006970 | A262051 | A262052 |

(union of all three) | | | |

Programs

PARI

isA375914(k) = k>1 && !isprime(k) && gcd(k,10)==1 && Mod(5,k)^((k-1)/2)==kronecker(5,k)