A375915 Composite numbers k == 1, 9 (mod 10) such that 5^((k-1)/2) == 1 (mod k).

781, 1541, 1729, 5461, 5611, 6601, 7449, 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, 133141, 135201, 141361

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

			29539 is a term because 29539 = 109*271 is composite, 29539 == 9 (mod 10), and 5^((29539-1)/2) == 1 (mod 29539).
		

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 | this seq |

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

(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 | A375914 |

(union of first two) | | | |

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

Euler pseudoprimes | A006970 | A262051 | A262052 |

(union of all three) | | | |

Programs

PARI

isA375915(k) = (k>1) && !isprime(k) && (k%10==1 || k%10==9) && Mod(5,k)^((k-1)/2) == 1