A243402 - OEIS

%I #19 Sep 08 2019 09:19:04

%S 449,839,857,941,977,1109,1289,1607,1901,2591,2711,3041,3299,4007,

%T 4349,4721,5531,5849,6311,6779,6911,7451,7829,7907,8369,8597,8999,

%U 9419,9767,11351,12917,13421,14321,14969,15077,15131,15227,15551,15809,16649,16979,17021,17291,17417

%N Primes p such that p^10 - p^9 - p^8 - p^7 - p^6 - p^5 - p^4 - p^3 - p^2 - p - 1 is prime.

%C No terms end in a 3, since if p == 3 (mod 10), then p^10 - p^9 - p^8 - p^7 - p^6 - p^5 - p^4 - p^3 - p^2 - p - 1 == 5 (mod 10) and is therefore not prime. - _Michel Marcus_, Jun 25 2014

%H K. D. Bajpai, <a href="/A243402/b243402.txt">Table of n, a(n) for n = 1..11323</a>

%t Select[Prime[Range[2100]],PrimeQ[#^10-Total[#^Range[9]]-1]&] (* _Harvey P. Dale_, Sep 08 2019 *)

%o (Python)

%o import sympy

%o from sympy import isprime

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

%o (PARI) for(n=1,5*10^4,if(ispseudoprime(n)&&ispseudoprime(n^10-sum(i=0,9,n^i)),print1(n,", ")))

%Y Cf. A243318.

%K nonn

%O 1,1

%A _Derek Orr_, Jun 04 2014