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 A383636 #15 May 07 2025 11:24:53
%S A383636 1,6,30,54
%N A383636 Integers k such that there is no prime of the form x*y+1 with x+y=k.
%C A383636 If k is odd, one of x or y is even. If k is even, there are cases where both x and y are odd. There is no need to check them, since we know in advance that x*y + 1 is even. - _Ivan N. Ianakiev_, May 04 2025
%C A383636 It is very likely that there are no further terms.
%t A383636 fQ[n_]:=If[OddQ[n],Select[Range[n/2],PrimeQ[(#*(n-#))+1]&]=={},Select[Range[2,n/2,2],PrimeQ[(#*(n-#))+1]&]=={}]; Select[Range[100],fQ] (* _Ivan N. Ianakiev_, May 04 2025 *)
%o A383636 (PARI) isok(k) = for(i=1, k\2, if(isprime(i*(k-i)+1), return(0))); 1;
%Y A383636 Cf. A026728, A109905.
%K A383636 nonn,hard
%O A383636 1,2
%A A383636 _Michel Marcus_, May 03 2025