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 A143205 #23 Feb 16 2025 08:33:08
%S A143205 55,91,187,247,275,391,605,637,667,1147,1183,1375,1591,1927,2057,2491,
%T A143205 3025,3127,3179,3211,4087,4459,4693,4891,5767,6647,6655,6875,7387,
%U A143205 8281,8993,9991,10807,11227,12091,15125,15341,15379,17947,19343,22627,23707
%N A143205 Numbers having exactly two distinct prime factors p, q with q = p+6.
%C A143205 Subsequence of A007774.
%C A143205 A111192 is a subsequence.
%C A143205 Subsequence of A195118. - _Reinhard Zumkeller_, Sep 13 2011
%H A143205 Reinhard Zumkeller, <a href="/A143205/b143205.txt">Table of n, a(n) for n = 1..250</a>
%H A143205 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SexyPrimes.html">Sexy Primes</a>. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- _N. J. A. Sloane_, Mar 07 2021]
%H A143205 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.
%F A143205 A143201(a(n)) = 7.
%F A143205 A020639(a(n)) in A023201 and A006530(a(n)) in A046117.
%F A143205 A001221(a(n)) = 2.
%F A143205 Sum_{n>=1} 1/a(n) = Sum_{n>=1} 1/((A023201(n)+2)^2-9) = 0.058842810164... . - _Amiram Eldar_, Oct 26 2024
%e A143205 a(1) = 55 = 5 * 11 = A023201(1) * A046117(1).
%e A143205 a(2) = 91 = 7 * 13 = A023201(2) * A046117(2).
%e A143205 a(3) = 187 = 11 * 17 = A023201(3) * A046117(3).
%e A143205 a(4) = 247 = 13 * 19 = A023201(4) * A046117(4).
%e A143205 a(5) = 275 = 5^2 * 11 = A023201(1)^2 * A046117(1).
%e A143205 a(6) = 391 = 17 * 23 = A023201(5) * A046117(5).
%e A143205 a(7) = 605 = 5 * 11^2 = A023201(1) * A046117(1)^2.
%e A143205 a(8) = 637 = 7^2 * 13 = A023201(2)^2 * A046117(2).
%e A143205 a(9) = 667 = 23 * 29 = A023201(6) * A046117(6).
%e A143205 a(10) = 1147 = 31 * 37 = A023201(7) * A046117(7).
%t A143205 okQ[n_]:=Module[{fi=Transpose[FactorInteger[n]][[1]]},Length[fi]==2 && Last[fi]-First[fi]==6]; Select[Range[25000],okQ] (* _Harvey P. Dale_, Apr 18 2011 *)
%o A143205 (Haskell)
%o A143205 a143205 n = a143205_list !! (n-1)
%o A143205 a143205_list = filter f [1,3..] where
%o A143205 f x = length pfs == 2 && last pfs - head pfs == 6 where
%o A143205 pfs = a027748_row x
%o A143205 -- _Reinhard Zumkeller_, Sep 13 2011
%Y A143205 Cf. A001221, A006530, A007774, A020639, A023201, A027748, A046117, A111192, A143201, A195118.
%K A143205 nonn
%O A143205 1,1
%A A143205 _Reinhard Zumkeller_, Jul 30 2008