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A240173 Numbers n such that k^n - 2^k is not prime for any k.

%I A240173 #29 Oct 03 2024 03:50:14
%S A240173 1,2,13,43,45,51,53,55,57,63,72,77,81,84,85,89,93,103,108,117,121,129,
%T A240173 147,149,151,163,171,173,177,183,191,213,229,231,239,241,250,259,261,
%U A240173 263,273,283,286,291,321,331,333,344,345,351,353,361,373,381,390,399
%N A240173 Numbers n such that k^n - 2^k is not prime for any k.
%C A240173 Numbers n such that A245459(n) = 0.
%H A240173 Amiram Eldar, <a href="/A240173/b240173.txt">Table of n, a(n) for n = 1..64</a>
%F A240173 A245459(a(n)) = 0.
%o A240173 (Python)
%o A240173 import sympy
%o A240173 def a(n):
%o A240173   k = 2
%o A240173   count = 0
%o A240173   while k**n > 2**k:
%o A240173     if sympy.isprime(k**n-2**k):
%o A240173       count += 1
%o A240173     k += 1
%o A240173   return count
%o A240173 n = 1
%o A240173 while n < 1000:
%o A240173   if not a(n):
%o A240173     print(n, end=', ')
%o A240173   n += 1 # _Derek Orr_, Aug 02 2014
%Y A240173 Cf. A245459.
%K A240173 nonn
%O A240173 1,2
%A A240173 _Juri-Stepan Gerasimov_, Aug 02 2014
%E A240173 a(13)-a(34) from _Derek Orr_, Aug 02 2014
%E A240173 a(35) onwards from _Amiram Eldar_, Oct 03 2024