%I #10 Jun 05 2022 08:28:06

%S 9,561,10585,1729,488881,399001,2433601,1857241,6189121,549538081,

%T 50201089,14469841,86566959361,311963097601,369838909441,

%U 31929487861441,6389476833601,8493512837546881,31585234281457921,10120721237827201,289980482095624321,525025434548260801,91230634325542321

%N Smallest Euler-Jacobi pseudoprime to all natural bases up to prime(n) - 1 that is not a base prime(n) Euler-Jacobi pseudoprime.

%C An Euler-Jacobi pseudoprime to the base b is an odd composite number k such that gcd(b, k) = 1 and the Jacobi symbol (.,.) satisfies b^((k-1)/2) == (b,k) (mod k).

%C a(n) is coprime to A002110(n-1).

%C a(24) > 2^64. - _Daniel Suteu_, Jun 05 2022

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

%o (PARI) a(n) = my(b, p=factorback(primes(n-1))); forcomposite(k=9, oo, if(gcd(k, p)==1, b=2; while(Mod(b, k)^(k\2) == kronecker(b, k), b++); if(b==prime(n), return(k))));

%Y Cf. A002110, A007324, A047713, A285549, A354694.

%K nonn

%O 1,1

%A _Jinyuan Wang_, Jun 03 2022

%E a(13)-a(23) from _Daniel Suteu_, Jun 05 2022