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

20183, 20963, 14011, 26759, 7433, 45613, 4703, 21911, 26539, 18233, 6581, 4423, 7351, 37379, 55903, 25801, 4373, 6529, 35879, 119993, 22171, 12923, 10691, 52609, 14303, 20201, 16231, 21121, 103049, 17863, 6451, 34439, 50341, 76129, 3803, 23251, 15241, 14369

Offset

9,1

Comments

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.

Links

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

Example

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].

Mathematica

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 *)

Prog

(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

Crossrefs

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

Keyword

nonn,changed

Author

Labos Elemer, Mar 07 2000

Extensions

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

Name and offset corrected by Amiram Eldar, Mar 05 2025

Status

approved