9,1

The smallest distance between 18-twins [A052380(9)] is 18 and its minimal increment is 2.

a(n) = p is the first prime initiating [p, p+18, p+2n, p+2n+18] prime and [18, 2n-18, 18] d-pattern.

Amiram Eldar, Table of n, a(n) for n = 9..1008

a(11) = 14011 initiates prime quadruple [14011, 14029, 14033, 14051] and difference pattern [18, 4, 18].

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].

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 *)

(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

Cf. A031936, A052380, A052381, A053327.

Cf. A052350, A052351, A052352, A052353, A052354, A052355, A052356, A052357, A052359.

Sequence in context: A114613 A209878 A031682 * A052189 A075670 A053073

Adjacent sequences: A052355 A052356 A052357 * A052359 A052360 A052361

Labos Elemer, Mar 07 2000

a(21) corrected and missing terms inserted by Sean A. Irvine, Nov 07 2021

Name and offset corrected by Amiram Eldar, Mar 05 2025

approved