This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A121616 #18 Sep 08 2022 08:45:27
%S A121616 31,211,4651,61051,371281,723901,1803001,2861461,4329151,4925281,
%T A121616 7086451,7944301,14835031,19611901,23382031,44119351,54664711,
%U A121616 86548801,97792531,162478501,189882031,267217051,293109961,306740281,490099501
%N A121616 Primes of form (k+1)^5 - k^5 = A022521(k).
%C A121616 Might be called "Pentan primes" (in analogy with Cuban primes, of the form (n+1)^3-n^3), or "Nexus primes of order 5" (cf. link below).
%C A121616 Indices k such that Nexus number of order 5 (or A022521(k-1) = k^5 - (k-1)^5) is prime are listed in A121617 = {2, 3, 6, 11, 17, 20, 25, 28, 31, 32, 35, 36, 42, 45, 47, 55, 58, 65, 67, 76, 79, 86, 88, 89, 100,...}.
%C A121616 The last digit is always 1 because 5 is the Pythagorean prime A002144(1). a(1) = 31 is the Mersenne prime A000668(3).
%H A121616 Zak Seidov, <a href="/A121616/b121616.txt">Table of n, a(n) for n = 1..2000.</a>
%t A121616 Select[Table[n^5 - (n-1)^5, {n,1,200}],PrimeQ]
%t A121616 Select[Differences[Range[100]^5],PrimeQ] (* _Harvey P. Dale_, Nov 03 2021 *)
%o A121616 (Magma) [a: n in [0..110] | IsPrime(a) where a is (n+1)^5-n^5]; // _Vincenzo Librandi_, Jan 20 2020
%Y A121616 Cf. A022521, A000040, A000043, A002144, A000668, A002407, A121617, A121618, A121619, A121620.
%K A121616 nonn
%O A121616 1,1
%A A121616 _Alexander Adamchuk_, Aug 10 2006