cp's OEIS Frontend

A240693 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.

%I A240693 #14 Oct 11 2023 12:16:14
%S A240693 5,17,53,137,229,389,467,619,709,787,1091,1103,1213,1249,1433,1459,
%T A240693 1601,1993,2029,2039,2087,2089,2393,2687,3217,3299,3529,3547,3691,
%U A240693 3793,4019,4091,4099,4231,4507,4561,4679,5351,5399,5471,5521,5581,5669,5783,5813,5861,5939,6247,6841,6899,6961
%N A240693 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 A240693 These are the primes in A162862.
%H A240693 Jon E. Schoenfield, <a href="/A240693/b240693.txt">Table of n, a(n) for n = 1..10000</a>
%e A240693 5^10 + 5^9 + 5^8 + 5^7 + 5^6 + 5^5 + 5^4 + 5^3 + 5^2 + 5 + 1 = 12207031 is prime. Thus, 5 is a term of this sequence.
%t A240693 Select[Prime[Range[200]], PrimeQ[1 + Sum[#^i, {i, 10}]] &] (* _Alonso del Arte_, Apr 11 2014 *)
%t A240693 Select[Prime[Range[900]],PrimeQ[Total[#^Range[0,10]]]&] (* _Harvey P. Dale_, Oct 11 2023 *)
%o A240693 (PARI) for(n=1,10^4,if(ispseudoprime(n^10+n^9+n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1)&&ispseudoprime(n),print(n)))
%o A240693 (Python)
%o A240693 import sympy
%o A240693 from sympy import isprime
%o A240693 {print(n) for n in range(10**4) if isprime(n) and isprime(n**10+n**9+n**8+n**7+n**6+n**5+n**4+n**3+n**2+n+1)}
%Y A240693 Cf. A162862.
%K A240693 nonn
%O A240693 1,1
%A A240693 _Derek Orr_, Apr 10 2014