A375914 Base-5 Euler-Jacobi pseudoprimes: odd composite k coprime to 5 such that 5^((k-1)/2) == (5/k) (mod k), 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

1,1

Links

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

Example

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).

Mathematica

q[k_] := OddQ[k] && CoprimeQ[k, 5] && CompositeQ[k] && PowerMod[5, (k-1)/2, k] == Mod[JacobiSymbol[5, k], k]; Select[Range[135000], q] (* Amiram Eldar, Mar 21 2026 *)

Prog

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

Crossrefs

For a list of sequences related to Euler-Jacobi pseudoprimes and Euler pseudoprimes, see A306310.

Sequence in context: A139400 A115467 A338877 * A375915 A020231 A141390

Adjacent sequences: A375911 A375912 A375913 * A375915 A375916 A375917

Keyword

nonn,changed

Author

Jianing Song, Sep 02 2024

Status

approved