A052357 Least prime in A031934 (lesser of 16-twins) whose distance to the next 16-twin is 6*n.

3373, 32917, 2221, 13597, 3391, 37783, 4057, 13537, 8581, 41911, 6763, 7333, 10867, 12457, 1831, 2113, 14683, 37201, 6637, 17581, 25423, 37447, 11353, 11197, 20611, 22453, 57397, 1933, 50707, 37591, 11503, 39733, 2593, 122131, 22921, 9013, 17167, 10273, 9661

Offset

3,1

Comments

The smallest distance between 16-twins [A052380(8)] is 18 and its minimal increment is 6.

a(n) = p is the smallest prime introducing the prime quadruple [p, p+16, p+6n, p+6n+16], which has a difference pattern [16, 6n-16, 16].

Links

Amiram Eldar, Table of n, a(n) for n = 3..1002

Example

a(9) = p = 4057 gives [4057, 4073, 4111, 4127] quadruple and [16, 38, 16] distance pattern with 4 primes in the medial gap.

Mathematica

seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 16] // Flatten; pp = p[[i]]; dd = Differences[pp]/6 - 2; 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 + 16, 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

Crossrefs

Cf. A031934, A052380, A052381, A053326.

Cf. A052350, A052351, A052352, A052353, A052354, A052355, A052356, A052358, A052359.

Sequence in context: A139779 A031626 A117921 * A218908 A164521 A251153

Adjacent sequences: A052354 A052355 A052356 * A052358 A052359 A052360

Keyword

nonn,changed

Author

Labos Elemer, Mar 07 2000

Extensions

Incorrect 43207 removed and more terms from Sean A. Irvine, Nov 06 2021

Name and offset corrected by Amiram Eldar, Mar 05 2025

Status

approved