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A239429 Numbers n such that n^6+6 and n^6-6 are prime.

%I A239429 #23 May 22 2025 10:21:37
%S A239429 175,12635,18445,30275,32585,38885,41125,46235,53165,71785,74935,
%T A239429 92645,108115,117775,121625,146125,151655,173635,184765,191765,196175,
%U A239429 204505,208705,229775,237965,241255,243635,246365,283115,335755,344365,345485,352625,353395,354445
%N A239429 Numbers n such that n^6+6 and n^6-6 are prime.
%C A239429 All numbers are congruent to 35 mod 70.
%C A239429 Intersection of A109836 and A239414.
%H A239429 Harvey P. Dale, <a href="/A239429/b239429.txt">Table of n, a(n) for n = 1..1000</a>
%e A239429 175^6+6 = 28722900390631 is prime and 175^6-6 = 28722900390619 is prime. Thus, 175 is a member of this sequence.
%t A239429 Select[Range[35,360000,70],AllTrue[#^6+{6,-6},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 22 2020 *)
%o A239429 (Python)
%o A239429 import sympy
%o A239429 from sympy import isprime
%o A239429 def TwoBoth(x):
%o A239429   for k in range(10**6):
%o A239429     if isprime(k**x+x) and isprime(k**x-x):
%o A239429       print(k)
%o A239429 TwoBoth(6)
%Y A239429 Cf. A109836, A239414.
%K A239429 nonn
%O A239429 1,1
%A A239429 _Derek Orr_, Mar 20 2014