cp's OEIS Frontend

A052354 Least prime in A031928 (lesser of 10-twins) whose distance to the next 10-twin is 6*n.

%I A052354 #24 Mar 05 2025 01:55:58
%S A052354 409,691,787,547,2053,139,4861,283,181,25087,337,709,2917,829,14197,
%T A052354 919,3001,33589,2767,421,8221,1879,5179,1249,1471,10141,5011,20533,
%U A052354 4483,54091,13249,4663,27883,5869,41443,8599,23311,9049,40699,82591,3109,5323,44917,11971
%N A052354 Least prime in A031928 (lesser of 10-twins) whose distance to the next 10-twin is 6*n.
%C A052354 a(n) = p determines a prime quadruple [p, p+10, p+6n, p+6n+10] with difference pattern [10, 6n-10, 10].
%C A052354 The smallest distance between 10-twins [A052380(5)] is 12, while its increment is 6.
%C A052354 a(n) = p is the smallest of A031928 followed by the next 10-twin after a 6n distance.
%H A052354 Amiram Eldar, <a href="/A052354/b052354.txt">Table of n, a(n) for n = 2..1001</a>
%e A052354 a(3) = 691 results in [691, 701, 709, 719] quadruple and [10, 8, 10] difference pattern without primes in the median gap.
%e A052354 a(11) = 25087 yields [25087, 25097, 25153, 25163] and [10, 56, 10] with 5 primes in the middle gap.
%t A052354 seq[m_] := Module[{p = Prime[Range[m]], d, i, pp, dd, j}, d = Differences[p]; i = Position[d, 10] // Flatten; pp = p[[i]]; dd = Differences[pp]/6 - 1; j = TakeWhile[FirstPosition[dd, #] & /@ Range[Max[dd]] // Flatten, ! MissingQ[#] &]; pp[[j]]]; seq[10000] (* _Amiram Eldar_, Mar 05 2025 *)~
%o A052354 (PARI) list(len) = {my(s = vector(len), c = 0, p1 = 2, q1 = 0, q2, d); forprime(p2 = 3, , if(p2 == p1 + 10, q2 = p1; if(q1 > 0, d = (q2 - q1)/6 - 1; 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 A052354 Cf. A031928, A052380, A052381, A053323.
%Y A052354 Cf. A052350, A052351, A052352, A052353, A052355, A052356, A052357, A052358, A052359.
%K A052354 nonn
%O A052354 2,1
%A A052354 _Labos Elemer_, Mar 07 2000
%E A052354 Name and offset corrected by _Amiram Eldar_, Mar 05 2025