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

1,1

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

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

Example

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

Mathematica

q[k_] := MemberQ[{3, 7}, Mod[k, 10]] && CompositeQ[k] && PowerMod[5, (k-1)/2, k] == k-1; Select[Range[8*10^6], q] (* Amiram Eldar, Mar 21 2026 *)

Prog

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

Crossrefs

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

Sequence in context: A234460 A253745 A253752 * A252317 A250026 A374576

Adjacent sequences: A375913 A375914 A375915 * A375917 A375918 A375919

Keyword

nonn

Author

Jianing Song, Sep 02 2024

Status

approved