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 A052381 #17 Nov 08 2021 04:30:42
%S A052381 3,7,47,389,409,199,24749,3373,20183,46703,19867,16763,142811,14563,
%T A052381 69593,763271,276637,255767,363989,383179,247099,2130809,15370423,
%U A052381 3565931,458069,9401647,6314393,20823437,9182389,4911251,15442121
%N A052381 The smallest initial prime of 2 non-overlapping d-twin primes if the distance between pairs (D) is minimal (see A052380).
%C A052381 A prime quadruple (triple), {[p,p+d],[p+D,p+D+d]} is called a "non-overlapping" (disjoint or touching) pair of twins if D = distance >= d = difference "inside" twin.
%F A052381 Smallest p so that [p, p+2n], [p+min{D}, p+2n+min{D}] is a quadruple (or triple if d=min{D}) of consecutive primes.
%e A052381 If n=23, d=46, min{D}=48 then the first suitable quadruple of primes is [15370423, 15370469, 15370471, 15370517] with difference pattern [46, 2, 46]; if n=3, d=6, min{D}=6 then the first such triple is [47, 53, 53, 59] = [47, 53, 59] with difference pattern [6, 6].
%Y A052381 The first 10 terms here appear as initial terms in A052350-A052359.
%Y A052381 See also A052380, A031924-A031928, A053318-A053331, A052350-A052359, A047948, A001223.
%K A052381 nonn
%O A052381 1,1
%A A052381 _Labos Elemer_, Mar 13 2000
%E A052381 Corrected by _Jud McCranie_, Jan 04 2001
%E A052381 a(11) corrected by _Sean A. Irvine_, Nov 07 2021