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A354692 Smallest Euler-Jacobi pseudoprime to all natural bases up to prime(n) - 1 that is not a base prime(n) Euler-Jacobi pseudoprime.

%I A354692 #11 Feb 16 2025 08:34:03
%S A354692 9,561,10585,1729,488881,399001,2433601,1857241,6189121,549538081,
%T A354692 50201089,14469841,86566959361,311963097601,369838909441,
%U A354692 31929487861441,6389476833601,8493512837546881,31585234281457921,10120721237827201,289980482095624321,525025434548260801,91230634325542321
%N A354692 Smallest Euler-Jacobi pseudoprime to all natural bases up to prime(n) - 1 that is not a base prime(n) Euler-Jacobi pseudoprime.
%C A354692 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 A354692 a(n) is coprime to A002110(n-1).
%C A354692 a(24) > 2^64. - _Daniel Suteu_, Jun 05 2022
%H A354692 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Euler-JacobiPseudoprime.html">Euler-Jacobi Pseudoprime</a>.
%o A354692 (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 A354692 Cf. A002110, A007324, A047713, A285549, A354694.
%K A354692 nonn
%O A354692 1,1
%A A354692 _Jinyuan Wang_, Jun 03 2022
%E A354692 a(13)-a(23) from _Daniel Suteu_, Jun 05 2022