A354689 Smallest Euler pseudoprime to base n.

9, 341, 121, 341, 217, 185, 25, 9, 91, 9, 133, 65, 21, 15, 341, 15, 9, 25, 9, 21, 65, 21, 33, 25, 217, 9, 65, 9, 15, 49, 15, 25, 545, 21, 9, 35, 9, 39, 133, 39, 21, 451, 21, 9, 133, 9, 65, 49, 25, 21, 25, 51, 9, 55, 9, 33, 25, 57, 15, 341, 15, 9, 341, 9, 33, 65

Offset

1,1

Comments

An Euler pseudoprime to the base b is a composite number k which satisfies b^((k-1)/2) == +-1 (mod k).

Links

Table of n, a(n) for n=1..66.

Eric Weisstein's World of Mathematics, Euler Pseudoprime.

Formula

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

Prog

(PARI) a(n) = my(m); forcomposite(k=3, oo, if(k%2 && ((m=Mod(n, k)^(k\2))==1 || m==k-1), return(k)));
(Python)
from sympy import isprime
from itertools import count
def a(n): return next(k for k in count(3, 2) if not isprime(k) and ((r:=pow(n, (k-1)//2, k)) == 1 or r == k-1))
print([a(n) for n in range(1, 67)]) # Michael S. Branicky, Jun 03 2022

Crossrefs

Cf. A006970, A090086, A298756, A326614.

Sequence in context: A090087 A090085 A098650 * A098652 A110695 A157589

Adjacent sequences: A354686 A354687 A354688 * A354690 A354691 A354692

Keyword

nonn

Author

Jinyuan Wang, Jun 03 2022

Status

approved