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 A338578 #10 Nov 10 2024 09:25:21 %S A338578 2,3,5,11,17,19,29,43,47,83,109,199,283 %N A338578 Primes p such that (r-p)*(r-q) > r, where q and r are the next two primes. %C A338578 a(14) > 10^8 if it exists. %C A338578 As soon as the prime gap grows slow enough, for all large enough p we have (r-p)*(r-q) <= r, implying finiteness of this sequence. In particular, finiteness would follow from Cramer's conjecture. - _Max Alekseyev_, Nov 09 2024 %e A338578 a(5)=17 is a member because it is prime, the next two primes are 19 and 23, and (23-17)*(23-19)=24 > 23. %p A338578 p:= 0: q:=2:r:= 3: R:= NULL: %p A338578 while p < 10^4 do %p A338578 p:= q: q:= r: r:= nextprime(r); %p A338578 if (r-q)*(r-p) > r then R:= R, p; fi %p A338578 od: %p A338578 R; %Y A338578 Contains A338566. %Y A338578 Cf. A013632, A105161, A338577. %K A338578 nonn,more %O A338578 1,1 %A A338578 _Robert Israel_, Nov 03 2020