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 A052356 #24 Mar 05 2025 01:57:35
%S A052356 24749,293,3833,21467,23417,14159,3779,18353,773,4817,18959,2939,863,
%T A052356 7607,3677,8039,5939,2633,7727,13367,51839,51659,7043,5153,8447,26189,
%U A052356 1409,113,7853,1847,13859,43223,2423,24533,65867,50909,19763,15173,15527,86477,55229
%N A052356 Least prime in A031932 (lesser of 14-twins) whose distance to the next 14-twin is 6*n.
%C A052356 The smallest distance between 14-twins [A052380(7)] is 18 and its minimal increment is 6.
%C A052356 a(n) = p is the first prime initiating [p, p+14, p+6n, p+6n+14] quadruple and prime difference pattern of [14, 6n-14, 14].
%H A052356 Amiram Eldar, <a href="/A052356/b052356.txt">Table of n, a(n) for n = 3..1002</a>
%e A052356 n = 4 results in [293,307,317,331] primes pattern and [14,24,14] difference pattern with 2 further primes (311 and 313) in the central gap.
%t A052356 seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 14] // Flatten; pp = p[[i]]; dd = Differences[pp]/6 - 2; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[10000] (* _Amiram Eldar_, Mar 05 2025 *)
%o A052356 (PARI) list(len) = {my(s = vector(len), c = 0, p1 = 2, q1 = 0, q2, d); forprime(p2 = 3, , if(p2 == p1 + 14, q2 = p1; if(q1 > 0, d = (q2 - q1)/6 - 2; if(d <= len && s[d] == 0, c++; s[d] = q1; if(c == len, return(s)))); q1 = q2); p1 = p2);} \\ _Amiram Eldar_, Mar 05 2025
%Y A052356 Cf. A031932, A052380, A052381, A053325.
%Y A052356 Cf. A052350, A052351, A052352, A052353, A052354, A052355, A052357, A052358, A052359.
%K A052356 nonn
%O A052356 3,1
%A A052356 _Labos Elemer_, Mar 07 2000
%E A052356 Name and offset corrected by _Amiram Eldar_, Mar 05 2025