A243298 Numbers k such that k^9 - k^8 - k^7 - k^6 - k^5 - k^4 - k^3 - k^2 - k - 1 is prime.

4, 16, 18, 28, 76, 84, 88, 118, 146, 180, 258, 272, 274, 282, 316, 380, 384, 400, 462, 464, 468, 476, 548, 586, 588, 610, 616, 644, 646, 702, 708, 756, 786, 810, 826, 944, 954, 956, 988, 1000, 1016, 1052, 1104, 1138, 1166, 1178, 1194, 1212, 1226, 1240, 1258, 1356

Offset

1,1

Comments

a(n) is even for all n.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2173

Example

4^9-4^8-4^7-4^6-4^5-4^4-4^3-4^2-4-1 = 174763 is prime. Thus, 4 is a member of this sequence.

Prog

(Python)
import sympy
from sympy import isprime
{print(n, end=', ') for n in range(10**4) if isprime(n**9-n**8-n**7-n**6-n**5-n**4-n**3-n**2-n-1)}
(Python)
from sympy import isprime
A243298_list, m = [], [362880, -1491840, 2464560, -2082240, 945000, -220248, 22560, -680, 1, -1]
for n in range(1, 10**5+1):
    for i in range(9):
        m[i+1]+= m[i]
    if isprime(m[-1]):
        A243298_list.append(n)
 # Chai Wah Wu, Nov 06 2014
(PARI) for(n=1, 10^3, if(ispseudoprime(n^9-sum(i=0, 8, n^i)), print1(n, ", ")))
(PARI) is(n)=isprime(n^9 - (n^9-1)/(n-1))
list(lim)=my(v=List()); forstep(n=4, lim, 2, if(is(n), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Mar 01 2025

Crossrefs

Sequence in context: A166620 A363084 A224705 * A139719 A117102 A077476

Adjacent sequences: A243295 A243296 A243297 * A243299 A243300 A243301

Keyword

nonn

Author

Derek Orr, Jun 02 2014

Status

approved