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A048950 Base 3 Euler-Jacobi pseudoprimes. 3

%I

%S 121,703,1729,1891,2821,3281,7381,8401,8911,10585,12403,15457,15841,

%T 16531,18721,19345,23521,24661,28009,29341,31621,41041,44287,46657,

%U 47197,49141,50881,52633,55969,63139,63973,74593,75361,79003,82513

%N Base 3 Euler-Jacobi pseudoprimes.

%C Odd composite n with gcd(n,3)=1 and 3^((n-1)/2) == (3,n) (mod n) where (.,.) is the Jacobi symbol. - _R. J. Mathar_, Jul 15 2012

%C The base 5 Euler-Jacobi pseudoprimes are 781, 1541, 1729, 5461, 5611, 6601, 7499,... - _R. J. Mathar_, Jul 15 2012

%H Amiram Eldar, <a href="/A048950/b048950.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Rotkiewicz, <a href="https://doi.org/10.1090/S0025-5718-1982-0658229-0">On Euler Lehmer pseudoprimes and strong Lehmer pseudoprimes with Parameters L, Q in arithmetic progressions</a>, Math. Comp 39 (159) (1982) 239-247.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Euler-JacobiPseudoprime.html">Euler-Jacobi Pseudoprime</a>.

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%t Select[Range[1, 10^5, 2], GCD[#, 3] == 1 && CompositeQ[#] && PowerMod[3, (# - 1)/2, #] == Mod[JacobiSymbol[3, #], #] &] (* _Amiram Eldar_, Jun 28 2019 *)

%o (PARI) is(n) = n%2==1 && gcd(n,3)==1 && Mod(3, n)^((n-1)/2)==kronecker(3,n)

%o forcomposite(c=1, 83000, if(is(c), print1(c, ", "))) \\ _Felix Fröhlich_, Jul 15 2019

%Y Cf. A047713 (base 2), A005935.

%K nonn

%O 1,1

%A _Eric W. Weisstein_

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Last modified September 17 16:57 EDT 2019. Contains 327136 sequences. (Running on oeis4.)