A057845 Numbers k such that k | 4^k + 2^k + 1.

1, 7, 49, 343, 2359, 2401, 16513, 16807, 115591, 117649, 794983, 809137, 8235433, 5564881, 5663959, 5764801, 38954167, 39647713, 40353607, 100170217, 267909271, 272679169, 277533991, 282475249, 701191519, 1636091527, 1875364897, 1908754183, 1942737937, 1977326743

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Mathematica

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

Prog

(PARI) isok(n) = Mod(4, n)^n + Mod(2, n)^n == -1 \\ Andrew Howroyd, Oct 30 2025
(Python)
from itertools import count, islice
def A057845_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda k: (a:=pow(2, k, k))*(a+1)%k == k-1, count(max(startvalue, 1)))
A057845_list = list(islice(A057845_gen(), 30)) # Chai Wah Wu, Jun 19 2026

Crossrefs

Cf. A001576.

Sequence in context: A057833 A014949 A228738 * A269617 A269581 A269433

Adjacent sequences: A057842 A057843 A057844 * A057846 A057847 A057848

Keyword

nonn,changed

Author

Robert G. Wilson v, Nov 09 2000

Extensions

a(14) onward from Andrew Howroyd, Oct 30 2025

Status

approved