cp's OEIS Frontend

A052359 Least prime in A031938 (lesser of primes differing by 20) whose distance to the next 20-twin is 6*n.

%I A052359 #29 Mar 05 2025 02:00:17
%S A052359 46703,37223,65147,20369,63929,71999,11597,11027,99767,93503,5903,
%T A052359 14087,115163,24821,104891,24923,11867,53381,65657,93581,99623,11447,
%U A052359 18461,126761,32213,27653,72797,5717,154247,54449,27827,10223,56747,18617,13421,10433,8543,60107
%N A052359 Least prime in A031938 (lesser of primes differing by 20) whose distance to the next 20-twin is 6*n.
%C A052359 The smallest distance between 20-twins is 24 [= A052380(10)], while its minimal increment is 6.
%C A052359 a(n) = p starts [p, p+20, p+6n, p+6n+20] and [20, 6n-20, 20] patterns of primes and their difference.
%C A052359 a(n) = p is the smallest prime which starts a [p, p+20] twin followed by the next [p+6n, p+6n+20] twin.
%H A052359 Amiram Eldar, <a href="/A052359/b052359.txt">Table of n, a(n) for n = 4..1003</a>
%e A052359 For n = 4, a(4) = 46703 results in prime quadruple [46703, 46723, 46727, 46747] and difference pattern [20, 4, 20].
%e A052359 For n = 14, a(14) = 5903 yields prime quadruple [5903, 5923, 5987, 6007] with 4 primes in the medial gap, and difference pattern [20, 64, 20].
%t A052359 seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 20] // Flatten; pp = p[[i]]; dd = Differences[pp]/6 - 3; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[15000] (* _Amiram Eldar_, Mar 05 2025 *)
%o A052359 (PARI) list(len) = {my(s = vector(len), c = 0, p1 = 2, q1 = 0, q2, d); forprime(p2 = 3, , if(p2 == p1 + 20, q2 = p1; if(q1 > 0, d = (q2 - q1)/6 - 3; 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 A052359 Cf. A031938, A052380, A052381, A053331.
%Y A052359 Cf. A052350, A052351, A052352, A052353, A052354, A052355, A052356, A052357, A052358.
%K A052359 nonn
%O A052359 4,1
%A A052359 _Labos Elemer_, Mar 07 2000
%E A052359 Offset changed to 1 by _Michel Marcus_, Apr 30 2019
%E A052359 Name and offset corrected by _Amiram Eldar_, Mar 05 2025