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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).

%I A375914 #19 Sep 07 2024 16:03:33
%S A375914 781,1541,1729,5461,5611,6601,7449,7813,11041,12801,13021,14981,15751,
%T A375914 15841,21361,24211,25351,29539,38081,40501,41041,44801,47641,53971,
%U A375914 67921,75361,79381,90241,100651,102311,104721,106201,106561,112141,113201,115921,121463,133141
%N 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).
%H A375914 Jianing Song, <a href="/A375914/b375914.txt">Table of n, a(n) for n = 1..1000</a>
%e A375914 781 is a term because 781 = 11*71 is composite, (5/781) = 1, and 5^((781-1)/2) == 1 (mod 781).
%e A375914 7813 is a term because 7813 = 13*601 is composite, (5/7813) = -1, and 5^((7813-1)/2) == -1 (mod 7813).
%o A375914 (PARI) isA375914(k) = k>1 && !isprime(k) && gcd(k,10)==1 && Mod(5,k)^((k-1)/2)==kronecker(5,k)
%Y A375914                                    |        b=2        |   b=3   |   b=5    |
%Y A375914 -----------------------------------+-------------------+---------+----------+
%Y A375914   (b/k)=1, b^((k-1)/2)==1 (mod k)  |      A006971      | A375917 | A375915  |
%Y A375914 -----------------------------------+-------------------+---------+----------+
%Y A375914  (b/k)=-1, b^((k-1)/2)==-1 (mod k) | A244628 U A244626 | A375918 | A375916  |
%Y A375914 -----------------------------------+-------------------+---------+----------+
%Y A375914  b^((k-1)/2)==-(b/k) (mod k), also |      A306310      | A375490 | A375816  |
%Y A375914  (b/k)=-1, b^((k-1)/2)==1 (mod k)  |                   |         |          |
%Y A375914 -----------------------------------+-------------------+---------+----------+
%Y A375914      Euler-Jacobi pseudoprimes     |      A047713      | A048950 | this seq |
%Y A375914        (union of first two)        |                   |         |          |
%Y A375914 -----------------------------------+-------------------+---------+----------+
%Y A375914         Euler pseudoprimes         |      A006970      | A262051 | A262052  |
%Y A375914        (union of all three)        |                   |         |          |
%K A375914 nonn
%O A375914 1,1
%A A375914 _Jianing Song_, Sep 02 2024