A243400 - OEIS

%I #8 Oct 13 2023 15:59:43

%S 5,7,17,37,79,157,239,269,277,359,419,449,467,557,677,739,787,829,857,

%T 977,1319,1399,1597,1657,2069,2269,2297,2377,2437,2459,2819,2969,2999,

%U 3019,3137,3299,3389,3407,3967,4007,4099,4357,4547,4729,4987,5179,5419,5569,5779,6637

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

%C a(1) = 5 is the only term that ends in a 5. It is unknown if any term will end in a 3 or 1.

%C In the first 100,000 primes, no term ends in a 3 or 1. - _Harvey P. Dale_, Oct 13 2023

%e 5 is prime and 5^6 - 5^5 - 5^4 - 5^3 - 5^2 - 5 - 1 = 11719 is prime. Thus 5 is a member of this sequence.

%t Select[Prime[Range[1000]],PrimeQ[#^6-Total[#^Range[0,5]]]&] (* _Harvey P. Dale_, Oct 13 2023 *)

%o (Python)

%o import sympy

%o from sympy import isprime

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

%o (PARI) for(n=1,10^4,if(ispseudoprime(n)&&ispseudoprime(n^6-sum(i=0,5,n^i)),print1(n,", ")))

%Y Cf. A243300.

%K nonn

%O 1,1

%A _Derek Orr_, Jun 04 2014