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%I #23 Sep 08 2022 08:45:58
%S 65537,4338014017,2973697798081,36054040477057,314707907280257,
%T 8746361693522261761,4441930186581050471617,1936348941361814438534657,
%U 8260002645666200230661441,157512780598351804823277697,684655198104511486296198721,21770695412796292350304592257
%N Primes of the form k^16 + (k+1)^16.
%C Prime 16-dimensional centered cube numbers. This is to dimension 16 as A194155 is to dimension 8 and as A152913 is to dimension 4.
%H Vincenzo Librandi, <a href="/A194185/b194185.txt">Table of n, a(n) for n = 1..3000</a>
%e a(1) = 1^16 + (1+1)^16 = 65537 = A100266(2).
%e a(2) = 3^16 + (3+1)^16 = 4338014017 = A100266(3).
%e a(3) = 5^16 + (5+1)^16 = 2973697798081 = A100266(4).
%e a(4) = 6^16 + (6+1)^16 = 36054040477057 = A100266(5).
%e a(5) = 7^16 + (7+1)^16 = 314707907280257 = A100266(6).
%e a(6) = 14^16 + (14+1)^16 = 8746361693522261761 = A100266(11).
%e a(7) = 21^16 + (21+1)^16 = 4441930186581050471617 = A100266(22).
%t Select[Table[n^16+(n+1)^16,{n,0,800}],PrimeQ] (* _Vincenzo Librandi_, Dec 07 2011 *)
%t Select[Total/@Partition[Range[60]^16,2,1],PrimeQ] (* _Harvey P. Dale_, Dec 07 2017 *)
%o (Magma) [ a: n in [1..100] | IsPrime(a) where a is n^16+(n+1)^16 ]; // _Vincenzo Librandi_, Dec 07 2011
%Y Cf. A000040, A154535, A100266, A152913, A194155.
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Aug 18 2011
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