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A326614 Smallest Euler-Jacobi pseudoprime to base n.

%I A326614 #25 Jul 19 2019 15:02:20
%S A326614 9,561,121,341,781,217,25,9,91,9,133,91,85,15,1687,15,9,25,9,21,221,
%T A326614 21,169,25,217,9,121,9,15,49,15,25,545,33,9,35,9,39,133,39,21,451,21,
%U A326614 9,481,9,65,49,25,49,25,51,9,55,9,55,25,57,15,481,15,9,529,9,33,65,33,25,35,69,9
%N A326614 Smallest Euler-Jacobi pseudoprime to base n.
%C A326614 a(n) = 9 for n == 1 or 8 mod 9 (see A056020).
%H A326614 Richard N. Smith, <a href="/A326614/b326614.txt">Table of n, a(n) for n = 1..5000</a>
%H A326614 Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%E2%80%93Jacobi_pseudoprime">Euler-Jacobi pseudoprime</a>
%t A326614 ejpspQ[n_,b_] := CoprimeQ[n,b] && CompositeQ[n] && Mod[b^((n - 1)/2) - JacobiSymbol[b, n], n] == 0; leastEJpsp[b_] := Module[{k=9}, While[!ejpspQ[k, b], k+=2]; k]; Array[leastEJpsp, 100] (* _Amiram Eldar_, Jul 15 2019 *)
%o A326614 (PARI) isok(k, n) = ((k%2==1) && (gcd(k, n)==1) && Mod(n, k)^((k-1)/2)==kronecker(n, k) && !isprime(k));
%o A326614 a(n) = my(k=2); while (! isok(k, n), k++); k; \\ _Michel Marcus_, Jul 15 2019
%Y A326614 Cf. A047713, A048950, A090086 (least Fermat pseudoprime to base n), A298756 (least strong pseudoprime to base n).
%K A326614 nonn
%O A326614 1,1
%A A326614 _Richard N. Smith_, Jul 14 2019