This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102331 #15 Feb 18 2025 04:04:23
%S A102331 13147,14407,114757,132607,231547,353317,459607,476587,568987,601747,
%T A102331 652357,724627,794137,861547,904777,1010407,1094437,1140847,1147567,
%U A102331 1170007,1270417,1424557,1441327,1477027,1604497,1646287,1673377,2043397,2078707,2126767,2130367
%N A102331 Initial members of quintuplets (p, p+4, p+12, p+16, p+24) of consecutive primes with the corresponding difference pattern is {4,8,4,8}.
%C A102331 Generalization of A022007. These primes are congruent to 7 modulo 10, so the realization of longer prime-difference pattern = {4,8,4,8,4} is not already possible because the sum = 4+8+4+8+4 = 28. Consequently, 10k+7+28 = 10m+5 cannot be a prime. Thus analogous generalization of A022008 is possible only with restrictions. See also Comment in A102335.
%H A102331 Amiram Eldar, <a href="/A102331/b102331.txt">Table of n, a(n) for n = 1..10000</a>
%F A102331 a(n) == 7 (mod 30). - _Amiram Eldar_, Feb 18 2025
%e A102331 The prime 13147 is followed by the primes {13151, 13159, 13163, 13171}. Observe that these patterns start and end with primes of the form 10k+7 and 10m+1, respectively.
%t A102331 Select[Partition[Prime[Range[158000]], 5, 1], Differences[#] == {4, 8, 4, 8} &][[;;, 1]] (* _Amiram Eldar_, Feb 18 2025 *)
%o A102331 (PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 8 && p4 - p3 == 4 && p5 - p4 == 8, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 18 2025
%Y A102331 Cf. A001223, A022007, A022008, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A102335.
%K A102331 nonn
%O A102331 1,1
%A A102331 _Labos Elemer_, Jan 07 2005