A366930 a(n) is the smallest odd composite k such that n^((k+1)/2) == n (mod k).

9, 9, 341, 121, 341, 65, 15, 21, 9, 9, 9, 33, 33, 21, 21, 15, 15, 9, 9, 9, 21, 15, 21, 33, 25, 15, 9, 9, 9, 21, 15, 15, 25, 33, 21, 9, 9, 9, 57, 39, 15, 21, 21, 21, 9, 9, 9, 65, 21, 21, 21, 15, 39, 9, 9, 9, 21, 21, 57, 145, 15, 15, 9, 9, 9, 33, 15, 33, 25, 21

Offset

0,1

Comments

If this sequence is bounded, then it is periodic with period P = LCM(A), where A is the set of all (pairwise distinct) terms.

Note that n^((1729+1)/2) == n (mod 1729) for every n >= 0, where 1729 is the smallest absolute Euler pseudoprime (A033181).

Thus a(n) <= 1729. So, as said, this sequence is periodic.

What is its period?

The period P of this sequence may be longer than the period of Euler primary pretenders (A309316), namely P > 41#*571#/4 (248 digits).

Links

Table of n, a(n) for n=0..69.

Formula

a(n) >= A309316(n).

Mathematica

a[n_] := Module[{k = 9}, While[PrimeQ[k] || PowerMod[n, (k + 1)/2, k] != Mod[n, k], k += 2]; k]; Array[a, 100, 0] (* Amiram Eldar, Nov 01 2023 *)

Prog

(PARI) a(n) = my(k=3); while (isprime(k) || Mod(n, k)^((k+1)/2) != n, k+=2); k; \\ Michel Marcus, Nov 01 2023

Crossrefs

Cf. A033181, A309316, A366973, A366982.

Sequence in context: A353182 A171738 A309316 * A124116 A213154 A226050

Adjacent sequences: A366927 A366928 A366929 * A366931 A366932 A366933

Keyword

nonn

Author

Thomas Ordowski, Nov 01 2023

Status

approved