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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).
9
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
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).
PROG
(PARI) isA375914(k) = k>1 && !isprime(k) && gcd(k, 10)==1 && Mod(5, k)^((k-1)/2)==kronecker(5, k)
CROSSREFS
| b=2 | b=3 | b=5 |
-----------------------------------+-------------------+---------+----------+
(b/k)=1, b^((k-1)/2)==1 (mod k) | A006971 | A375917 | A375915 |
-----------------------------------+-------------------+---------+----------+
(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 | this seq |
(union of first two) | | | |
-----------------------------------+-------------------+---------+----------+
Euler pseudoprimes | A006970 | A262051 | A262052 |
(union of all three) | | | |
Sequence in context: A139400 A115467 A338877 * A375915 A020231 A141390
KEYWORD
nonn
AUTHOR
Jianing Song, Sep 02 2024
STATUS
approved