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 A262935 #24 Apr 09 2016 17:07:58
%S A262935 1,2,4,6,10,12,16,18,28,30,34,42,46,48,58,88,90,94,124,130,136,154,
%T A262935 162,168,172,178,202,216,258,264,294,342,352,354,364,366,370,378,396,
%U A262935 408
%N A262935 Increasing distances of lonely twin primes pairs to nearest prime.
%F A262935 a(n) = d if ( (p(i+1) = p(i)+2) AND (d = min(p(i+2)-p(i+1), p(i)-p(i-1)) > a(n-1)) ), where a(0) = 0, p(k) = prime(k) = A000040(k).
%e A262935 (3,5) is a twin primes pair, min(7-5, 3-2)=1, therefore a(1)=1.
%e A262935 (5,7) is a twin primes pair, min(11-7, 5-3)=2>1, therefore a(2)=2.
%e A262935 (11,13) is a twin primes pair, min(17-13, 11-7)=4>2, therefore a(3)=4.
%o A262935 (PARI) {m=0; q=5; s=3; t=2; forprime(p=6, 10^9, if((q-s==2) && (min(p-q, s-t)>m), m=min(p-q, s-t); print1(m, ", ") ); t=s; s=q; q=p;)}
%Y A262935 Cf. A035789, A069453, A069455, A262936.
%K A262935 nonn
%O A262935 1,2
%A A262935 _Dmitry Petukhov_, Oct 04 2015