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Numbers n such that n^6+6 and n^6-6 are prime.
1

%I #21 Nov 22 2020 15:03:42

%S 175,12635,18445,30275,32585,38885,41125,46235,53165,71785,74935,

%T 92645,108115,117775,121625,146125,151655,173635,184765,191765,196175,

%U 204505,208705,229775,237965,241255,243635,246365,283115,335755,344365,345485,352625,353395,354445

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

%C All numbers are congruent to 35 mod 70.

%C Intersection of A109836 and A239414.

%H Harvey P. Dale, <a href="/A239429/b239429.txt">Table of n, a(n) for n = 1..1000</a>

%e 175^6+6 = 28722900390631 is prime and 175^6-6 = 28722900390619 is prime. Thus, 175 is a member of this sequence.

%t Select[Range[35,360000,70],AllTrue[#^6+{6,-6},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 22 2020 *)

%o (Python)

%o import sympy

%o from sympy import isprime

%o def TwoBoth(x):

%o ..for k in range(10**6):

%o ....if isprime(k**x+x) and isprime(k**x-x):

%o ......print(k)

%o TwoBoth(6)

%Y Cf. A109836, A239414.

%K nonn

%O 1,1

%A _Derek Orr_, Mar 20 2014