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

9, 561, 10585, 1729, 488881, 399001, 2433601, 1857241, 6189121, 549538081, 50201089, 14469841, 86566959361, 311963097601, 369838909441, 31929487861441, 6389476833601, 8493512837546881, 31585234281457921, 10120721237827201, 289980482095624321, 525025434548260801, 91230634325542321

Offset: 1

Author

Jinyuan Wang, Jun 03 2022

Keywords

• nonn

Comments

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).

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

a(24) > 2^64. - Daniel Suteu, Jun 05 2022

Links

• Eric Weisstein's World of Mathematics, Euler-Jacobi Pseudoprime.

Crossrefs

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

Programs

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))));

Extensions

a(13)-a(23) from Daniel Suteu, Jun 05 2022