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 A158979 #14 Aug 09 2023 19:02:13
%S A158979 2,3,4,5,8,7,10,9,10,13,16,13,14,15,22,17,20,23,24,29,38,29,26,41,26,
%T A158979 27,28,33,34,37,32,37,34,35,52,37,38,39,46,41,50,53,44,47,58,55,50,49,
%U A158979 60,61,62,61,56,55,58,59,68,61,62,73,66,77,64,67,84,71
%N A158979 a(n) is the smallest number > n such that n^4 + a(n)^4 is prime.
%C A158979 For exponent 2 instead of 4 see A089489: Pythagorean triple has a prime hypotenuse.
%C A158979 Corresponding sequences with odd exponent u are impossible: x^u + y^u has factor x+y.
%C A158979 a(2k-1) is even, a(2k) is odd, a(n)-n is odd.
%C A158979 Conjecture: a(n) exists for all n, i.e., the sequence is well-defined and infinite.
%C A158979 Conjecture: a(n)-n = 1 for infinitely many n.
%C A158979 The largest value of a(n)-n for n <= 100 occurs at n = 90: 121-90 = 31.
%C A158979 a(n)-n = 1 for 35 values of n <= 100.
%H A158979 Harvey P. Dale, <a href="/A158979/b158979.txt">Table of n, a(n) for n = 1..1000</a>
%e A158979 1^4 + 2^4 = 17 is prime, so a(1) = 2.
%e A158979 2^4 + 3^4 = 97 is prime, so a(2) = 3.
%e A158979 5^4 + 6^4 = 1921 = 17*113, 5^4 + 7^4 = 3026 = 2*17*89, 5^4 + 8^4 = 4721 is prime, so a(5) = 8.
%t A158979 sn[n_]:=Module[{k=n+1,n4=n^4},While[CompositeQ[n4+k^4],k++];k]; Array[sn,80] (* _Harvey P. Dale_, Aug 09 2023 *)
%o A158979 (Magma) S:=[]; for n in [1..72] do q:=n^4; k:=n+1; while not IsPrime(q+k^4) do k+:=1; end while; Append(~S, k); end for; S; // _Klaus Brockhaus_, Apr 12 2009
%Y A158979 Cf. A089489.
%K A158979 easy,nonn
%O A158979 1,1
%A A158979 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 01 2009
%E A158979 Edited and entries verified by _Klaus Brockhaus_, Apr 12 2009
%E A158979 Corrected by _Harvey P. Dale_, Aug 09 2023