OFFSET
1,1
COMMENTS
Odd composite k with gcd(k,3) = 1 and 3^((k-1)/2) == (3,k) (mod k) where (.,.) is the Jacobi symbol. - R. J. Mathar, Jul 15 2012
The base 5 Euler-Jacobi pseudoprimes are 781, 1541, 1729, 5461, 5611, 6601, 7449, ... - R. J. Mathar, Jul 15 2012 [Typo fixed; this is A375914. - Jianing Song, Sep 02 2024]
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
A. Rotkiewicz, On Euler Lehmer pseudoprimes and strong Lehmer pseudoprimes with Parameters L, Q in arithmetic progressions, Math. Comp 39 (159) (1982) 239-247.
Eric Weisstein's World of Mathematics, Euler-Jacobi Pseudoprime.
MATHEMATICA
Select[Range[1, 10^5, 2], GCD[#, 3] == 1 && CompositeQ[#] && PowerMod[3, (# - 1)/2, #] == Mod[JacobiSymbol[3, #], #] &] (* Amiram Eldar, Jun 28 2019 *)
PROG
(PARI) is(n) = n%2==1 && gcd(n, 3)==1 && Mod(3, n)^((n-1)/2)==kronecker(3, n)
forcomposite(c=1, 83000, if(is(c), print1(c, ", "))) \\ Felix Fröhlich, Jul 15 2019
CROSSREFS
Cf. A005935.
| b=2 | b=3 | b=5 |
-----------------------------------+-------------------+----------+---------+
-----------------------------------+-------------------+----------+---------+
-----------------------------------+-------------------+----------+---------+
(b/k)=-1, b^((k-1)/2)==1 (mod k) | | | |
-----------------------------------+-------------------+----------+---------+
(union of first two) | | | |
-----------------------------------+-------------------+----------+---------+
(union of all three) | | | |
KEYWORD
nonn
AUTHOR
STATUS
approved