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A052358 Least prime in A031936 (lesser of 18-twins) whose distance to the next 18-twin is 2*n.

%I A052358 #23 Mar 05 2025 01:59:12
%S A052358 20183,20963,14011,26759,7433,45613,4703,21911,26539,18233,6581,4423,
%T A052358 7351,37379,55903,25801,4373,6529,35879,119993,22171,12923,10691,
%U A052358 52609,14303,20201,16231,21121,103049,17863,6451,34439,50341,76129,3803,23251,15241,14369
%N A052358 Least prime in A031936 (lesser of 18-twins) whose distance to the next 18-twin is 2*n.
%C A052358 The smallest distance between 18-twins [A052380(9)] is 18 and its minimal increment is 2.
%C A052358 a(n) = p is the first prime initiating [p, p+18, p+2n, p+2n+18] prime and [18, 2n-18, 18] d-pattern.
%H A052358 Amiram Eldar, <a href="/A052358/b052358.txt">Table of n, a(n) for n = 9..1008</a>
%e A052358 a(11) = 14011 initiates prime quadruple [14011, 14029, 14033, 14051] and difference pattern [18, 4, 18].
%e A052358 a(15) = 4703 specifies prime quadruple  [4703, 4721, 4133, 4151] which includes 2 primes (4723, 4729) in the center, and difference pattern [18, 28, 18].
%t A052358 seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 18] // Flatten; pp = p[[i]]; dd = Differences[pp]/2 - 8; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[12000] (* _Amiram Eldar_, Mar 05 2025 *)
%o A052358 (PARI) list(len) = {my(s = vector(len), c = 0, p1 = 2, q1 = 0, q2, d); forprime(p2 = 3, , if(p2 == p1 + 18, q2 = p1; if(q1 > 0, d = (q2 - q1)/2 - 8; 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 A052358 Cf. A031936, A052380, A052381, A053327.
%Y A052358 Cf. A052350, A052351, A052352, A052353, A052354, A052355, A052356, A052357, A052359.
%K A052358 nonn
%O A052358 9,1
%A A052358 _Labos Elemer_, Mar 07 2000
%E A052358 a(21) corrected and missing terms inserted by _Sean A. Irvine_, Nov 07 2021
%E A052358 Name and offset corrected by _Amiram Eldar_, Mar 05 2025