A194185 Primes of the form k^16 + (k+1)^16.

65537, 4338014017, 2973697798081, 36054040477057, 314707907280257, 8746361693522261761, 4441930186581050471617, 1936348941361814438534657, 8260002645666200230661441, 157512780598351804823277697, 684655198104511486296198721, 21770695412796292350304592257

Offset: 1

Author

Jonathan Vos Post, Aug 18 2011

Keywords

• nonn
• easy

Comments

Prime 16-dimensional centered cube numbers. This is to dimension 16 as A194155 is to dimension 8 and as A152913 is to dimension 4.

Examples

			a(1) = 1^16 + (1+1)^16 = 65537 = A100266(2).
a(2) = 3^16 + (3+1)^16 = 4338014017 = A100266(3).
a(3) = 5^16 + (5+1)^16 = 2973697798081 = A100266(4).
a(4) = 6^16 + (6+1)^16 = 36054040477057 = A100266(5).
a(5) = 7^16 + (7+1)^16 = 314707907280257 = A100266(6).
a(6) = 14^16 + (14+1)^16 = 8746361693522261761 = A100266(11).
a(7) = 21^16 + (21+1)^16 = 4441930186581050471617 = A100266(22).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A000040, A154535, A100266, A152913, A194155.

Programs

Magma

[ a: n in [1..100] | IsPrime(a) where a is n^16+(n+1)^16 ]; // Vincenzo Librandi, Dec 07 2011

Mathematica

Select[Table[n^16+(n+1)^16,{n,0,800}],PrimeQ] (* Vincenzo Librandi, Dec 07 2011 *)
Select[Total/@Partition[Range[60]^16,2,1],PrimeQ] (* Harvey P. Dale, Dec 07 2017 *)