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

1,1

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).

Links

Table of n, a(n) for n=1..38.

Example

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

Prog

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

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), | | | |

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: A115467 A338877 A375914 * A020231 A141390 A038477

Adjacent sequences: A375911 A375913 A375914 * A375916 A375917 A375918

Keyword

nonn,new

Author

Jianing Song, Sep 02 2024

Status

approved