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A375915
Composite numbers k == 1, 9 (mod 10) such that 5^((k-1)/2) == 1 (mod k).
9
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
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), 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
KEYWORD
nonn
AUTHOR
Jianing Song, Sep 02 2024
STATUS
approved