A346988 a(n) is the smallest k > n such that n^(k-n) == 1 (mod k).

2, 20737, 9299, 7, 13, 311, 15, 127, 17, 37, 14, 23, 17, 157, 106, 31, 29, 312953, 45, 95951, 41, 91, 33, 47, 28, 95, 35, 271, 35, 9629, 39, 311, 85, 397, 46, 71, 43, 1793, 95, 79, 61, 821, 51, 18881, 67, 103, 51, 12409, 73, 409969, 65, 87, 65, 71233, 63, 155, 65, 69, 87, 1962251, 91, 2443783, 155

Offset

1,1

Comments

Smallest k > n coprime to n such that n^k == n^n (mod k).

If a(n) is a prime p, then n^(n-1) == 1 (mod p).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Mathematica

a[n_] := Module[{k = n + 1}, While[PowerMod[n, k - n, k] != 1, k++]; k]; Array[a, 60] (* Amiram Eldar, Aug 10 2021 *)

Prog

(PARI) a(n) = my(k=n+1); while (Mod(n, k)^(k-n) != 1, k++); k; \\ Michel Marcus, Aug 10 2021
(Python)
def A346988(n):
    k, kn = n+1, 1
    while True:
        if pow(n, kn, k) == 1:
            return k
        k += 1
        kn += 1 # Chai Wah Wu, Aug 28 2021

Crossrefs

Cf. A173572, A242865, A344681.

Sequence in context: A124364 A173156 A214598 * A339476 A242959 A123692

Adjacent sequences: A346985 A346986 A346987 * A346989 A346990 A346991

Keyword

nonn

Author

Thomas Ordowski, Aug 10 2021

Extensions

More terms from Amiram Eldar, Aug 10 2021

Status

approved