A057842 Numbers k such that k | 6^k + 4^k + 2^k + 1.

1, 13, 4381, 560129, 606797, 3512659, 4102673, 26748149, 531653263, 1442296697, 3873360149, 604741570691, 2071864977379, 7493362805389

Offset

1,2

Comments

Numbers k that divide A074533(k)+1. - Michel Marcus, Oct 30 2025

Links

Table of n, a(n) for n=1..14.

Mathematica

Select[ Range[ 10^6 ], Mod[ PowerMod[ 6, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 2, #, # ] + 1, # ] == 0 & ]

Prog

(PARI) isok(n) = Mod(6, n)^n + Mod(4, n)^n + Mod(2, n)^n == -1 \\ Andrew Howroyd, Oct 30 2025
(Python)
from itertools import count, islice
def A057842_gen(startvalue=1): # generator of terms >= startvalue
    for k in count(max(startvalue, 1)):
        a, b = pow(2, k, k), pow(3, k, k)
        if a*(a+b+1)%k == k-1:
            yield k
A057842_list = list(islice(A057842_gen(), 7)) # Chai Wah Wu, Jun 19 2026

Crossrefs

Cf. A006521, A057839, A057840, A057845, A074533.

Sequence in context: A389277 A174310 A362659 * A203676 A023345 A249941

Adjacent sequences: A057839 A057840 A057841 * A057843 A057844 A057845

Keyword

nonn,more

Author

Robert G. Wilson v, Nov 09 2000

Extensions

a(6)-a(8) from Andrew Howroyd, Oct 30 2025

a(9)-a(14) from Jinyuan Wang, Jun 19 2026

Status

approved