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 A217030 #17 Jan 29 2024 19:22:31
%S A217030 237,427,1027,1101,1661,2723,2747,3173,3295,3669,3849,3873,3963,4087,
%T A217030 4227,4237,4667,4717,4897,5007,5017,5277,5837,6145,6249,6445,6697,
%U A217030 6757,6787,6943,7483,8373,9169,9183,9543,9673,9691,9903,10063,10135,10239,10523,10981
%N A217030 Semiprimes p such that next semiprime after p is p + 10.
%C A217030 First pair of successive semiprimes with gap 10 is {237 = 3*79, 247 = 13*19}. First triple of successive semiprimes with gaps 10 is {4227 = 3*1409, 4237 = 19*223, 4247 = 31*137}. First quadruple of successive semiprimes with gaps 10 is {63643 = 31*2053, 63653 = 53*1201, 63663 = 3*21221, 63673 = 41*1553}. First 5 successive semiprimes with gaps 10 are {1381951 = 103*13417, 1381961 = 7*197423, 1381971 = 3*460657, 1381981 = 17*81293, 1381991 = 13*106307}. First 6 successive semiprimes with gaps 10 are {16476607 = 7*2353801, 16476617 = 557*29581, 16476627 = 3*5492209, 16476637 = 3677*4481, 16476647 = 11*1497877, 16476657 = 3*5492219}.
%H A217030 Zak Seidov, <a href="/A217030/b217030.txt">Table of n, a(n) for n = 1..10000</a>
%t A217030 SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; t = Select[Range[11000], SemiPrimeQ[#] &]; t2 = Differences[t]; t[[Flatten[Position[t2, 10]]]] (* _T. D. Noe_, Sep 24 2012 *)
%t A217030 Select[Partition[Select[Range[11000],PrimeOmega[#]==2&],2,1],#[[2]]-#[[1]]==10&][[;;,1]] (* _Harvey P. Dale_, Jan 29 2024 *)
%o A217030 (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [n: n in [4..13000] | IsSemiprime(n) and IsSemiprime(n+10) and forall{n+i: i in [1..9] | not IsSemiprime(n+i)}]; // _Bruno Berselli_, Oct 01 2012
%Y A217030 Cf. A001358.
%K A217030 nonn
%O A217030 1,1
%A A217030 _Zak Seidov_, Sep 24 2012