A243318 Numbers n such that n^10 - n^9 - n^8 - n^7 - n^6 - n^5 - n^4 - n^3 - n^2 - n - 1 is prime.

15, 56, 65, 74, 87, 104, 132, 150, 171, 185, 186, 204, 225, 234, 360, 429, 449, 455, 459, 476, 485, 512, 675, 746, 770, 780, 795, 816, 836, 839, 840, 846, 857, 876, 902, 930, 939, 941, 944, 977, 1109, 1152, 1161, 1190, 1262, 1289, 1295, 1316, 1355, 1362, 1374, 1395, 1401, 1425

Offset: 1

Author

Derek Orr, Jun 03 2014

Keywords

• nonn

Examples

			15^10 - 15^9 - 15^8 - 15^7 - 15^6 - 15^5 - 15^4 - 15^3 - 15^2 - 15 - 1 = 535461077009 is prime. Thus 15 is a member of this sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2470

Crossrefs

Cf. A162862.

Programs

Magma

[n: n in [0..2000] | IsPrime(n^10-n^9-n^8-n^7-n^6- n^5-n^4-n^3-n^2-n-1)]; // Vincenzo Librandi, Dec 06 2016

Maple

A243318:=n->`if`(isprime(n^10-add(n^i, i=0..9)), n, NULL): seq(A243318(n), n=1..2*10^3); # Wesley Ivan Hurt, Dec 05 2016

Mathematica

Select[Range[2000], PrimeQ[#^10 - #^9 - #^8 - #^7 - #^6 - #^5 - #^4 - #^3 - #^2 - # - 1] &] (* Vincenzo Librandi, Dec 06 2016 *)

PARI

for(n=1, 10^4, if(ispseudoprime(n^10-sum(i=0, 9, n^i)), print1(n, ", ")))

Python

import sympy
from sympy import isprime
{print(n, end=', ') for n in range(10**4) if isprime(n**10-n**9-n**8-n**7-n**6-n**5-n**4-n**3-n**2-n-1)}

Python

from sympy import isprime
A243318_list, m = [], [3628800, -16692480, 31651200, -31827600, 18163440, -5826240, 971232, -69720, 1362, -2, -1]
for n in range(1, 10**5+1):
    for i in range(10):
        m[i+1]+= m[i]
    if isprime(m[-1]):
        A243318_list.append(n) # Chai Wah Wu, Nov 06 2014