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 A052377 #13 Nov 08 2021 04:30:35
%S A052377 389,479,1559,3209,8669,12269,12401,13151,14411,14759,21851,28859,
%T A052377 31469,33191,36551,39659,40751,50321,54311,64601,70229,77339,79601,
%U A052377 87671,99551,102539,110261,114749,114761,118661,129449,132611,136511
%N A052377 Primes followed by an [8,4,8]=[d,D-d,d] prime difference pattern of A001223.
%C A052377 A subsequence of A031926. [Corrected by _Sean A. Irvine_, Nov 07 2021]
%C A052377 a(n)=p, the initial prime of two consecutive 8-twins of primes as follows: [p,p+8] and [p+12,p+12+8], d=8, while the distance of the two 8-twins is 12 (minimal; see A052380(4/2)=12).
%C A052377 Analogous sequences are A047948 for d=2, A052378 for d=4, A052376 for d=10 and A052188-A052199 for d=6k, so that in the [d,D-d,d] difference patterns which follows a(n) the D-d is minimal(=0,2,4; here it is 4).
%F A052377 a(n) is the initial term of a [p, p+8, p+12, p+12+8] quadruple of consecutive primes.
%e A052377 p=1559 begins the [1559,1567,1571,1579] prime quadruple consisting of two 8-twins [1559,1567] and[1571,1579] which are in minimal distance, min{D}=1571-1559=12=A052380(8/2).
%Y A052377 Cf. A031926, A053325, A052380, A052376, A052378, A052188-A052190.
%K A052377 nonn
%O A052377 1,1
%A A052377 _Labos Elemer_, Mar 22 2000