A333430 a(n) is the n-th number m that divides n^m + 1 (or 0 if m does not exist).

1, 3, 10, 125, 21, 1379, 2810, 243, 3125, 30613, 729, 685633, 850, 183

Offset: 1

Author

Alois P. Heinz, Mar 20 2020

Keywords

• nonn
• hard
• more

Comments

a(15) > 10^19.

a(16) = 29623979969.

a(17) = 250.

a(19) = 13915.

a(15) <= 76717223012242243155874. - Jinyuan Wang, Mar 25 2020

From Jon E. Schoenfield, Aug 28 2021: (Start)

a(18) = 16983563041.

Next 20 terms after the first unknown term (a(15)): 29623979969, 250, 16983563041, 13915, 1143, 23426, 5608987, 2187, 75625, 25160213, 2709, 26803, a(28), 729, a(30), 2702258, 6633, 118810, 15625, 6379479. (End)

Crossrefs

Main diagonal of A333429.

Cf. A333433.

Programs

PARI

a(n) = {my(c=0, m=0); while(cJinyuan Wang, Mar 25 2020

Python

def a(n):
    if n == 1: return 1
    m = 0
    for c in range(1, n+1):
        m += 1
        while not (pow(n, m, m) + 1)%m == 0: m += 1
    return m
print([a(n) for n in range(1, 15)]) # Michael S. Branicky, Aug 28 2021

Formula

a(n) = A333429(n,n).