cp's OEIS Frontend

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.

A338578 Primes p such that (r-p)*(r-q) > r, where q and r are the next two primes.

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%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