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A052355 Least prime in A031930 (lesser of 12-twins) whose distance to the next 12-twin is 2*n.

%I A052355 #22 Mar 05 2025 01:56:26
%S A052355 199,7937,3331,3049,1511,1789,28607,7001,20599,2069,18257,46477,1201,
%T A052355 15569,1459,467,23087,23041,2399,6101,7057,6607,23801,3931,3499,9029,
%U A052355 5197,7841,3191,1237,3259,45767,4801,1811,1709,40867,23497,125441,5419,3989,18077,21787
%N A052355 Least prime in A031930 (lesser of 12-twins) whose distance to the next 12-twin is 2*n.
%C A052355 The smallest distance between 12-twins [A052380(6)] is 12 and its minimal increment is 2.
%C A052355 a(n) = p specifies a quadruple [p, p+12, p+2n, p+2n+12] with difference pattern of [12, 2n-12, 12].
%H A052355 Amiram Eldar, <a href="/A052355/b052355.txt">Table of n, a(n) for n = 6..1005</a>
%e A052355 a(7) = 7937 results in [7937, 7949, 7951, 7963] quadruple and [12, 2, 12] difference pattern.
%e A052355 a(10) = 1511 specifies [1511, 1523, 1531, 1543] quadruple and [12, 8, 12] difference pattern without prime in the central gap.
%t A052355 seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 12] // Flatten; pp = p[[i]]; dd = Differences[pp]/2 - 5; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[1q000] (* _Amiram Eldar_, Mar 05 2025 *)
%o A052355 (PARI) list(len) = {my(s = vector(len), c = 0, p1 = 2, q1 = 0, q2, d); forprime(p2 = 3, , if(p2 == p1 + 12, q2 = p1; if(q1 > 0, d = (q2 - q1)/2 - 5; 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 A052355 Cf. A031930, A052380, A052381, A053324.
%Y A052355 Cf. A052350, A052351, A052352, A052353, A052354, A052356, A052357, A052358, A052359.
%K A052355 nonn
%O A052355 6,1
%A A052355 _Labos Elemer_, Mar 07 2000
%E A052355 Name and offset corrected by _Amiram Eldar_, Mar 05 2025