A326614 Smallest Euler-Jacobi pseudoprime to base n.

9, 561, 121, 341, 781, 217, 25, 9, 91, 9, 133, 91, 85, 15, 1687, 15, 9, 25, 9, 21, 221, 21, 169, 25, 217, 9, 121, 9, 15, 49, 15, 25, 545, 33, 9, 35, 9, 39, 133, 39, 21, 451, 21, 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

Offset

1,1

Comments

a(n) = 9 for n == 1 or 8 mod 9 (see A056020).

Links

Richard N. Smith, Table of n, a(n) for n = 1..5000

Wikipedia, Euler-Jacobi pseudoprime

Mathematica

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 *)

Prog

(PARI) isok(k, n) = ((k%2==1) && (gcd(k, n)==1) && Mod(n, k)^((k-1)/2)==kronecker(n, k) && !isprime(k));
a(n) = my(k=2); while (! isok(k, n), k++); k; \\ Michel Marcus, Jul 15 2019

Crossrefs

Cf. A047713, A048950, A090086 (least Fermat pseudoprime to base n), A298756 (least strong pseudoprime to base n).

Sequence in context: A317347 A357229 A267548 * A007324 A354692 A373882

Adjacent sequences: A326611 A326612 A326613 * A326615 A326616 A326617

Keyword

nonn

Author

Richard N. Smith, Jul 14 2019

Status

approved