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A111192 Product of the n-th sexy prime pair.

%I A111192 #38 Aug 12 2025 02:35:58
%S A111192 55,91,187,247,391,667,1147,1591,1927,2491,3127,4087,4891,5767,7387,
%T A111192 9991,10807,11227,12091,17947,23707,25591,28891,30967,37627,38407,
%U A111192 51067,52891,55687,64507,67591,70747,75067,78391,96091,98587,111547,122491,126727,136891
%N A111192 Product of the n-th sexy prime pair.
%C A111192 Semiprime of the form 4*m^2-9 = (2*m-3)*(2*m+3). - _Vincenzo Librandi_, Jan 26 2016
%H A111192 Reinhard Zumkeller, <a href="/A111192/b111192.txt">Table of n, a(n) for n = 1..10000</a>
%H A111192 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].
%F A111192 a(n) = A023201(n) * A046117(n). - _Reinhard Zumkeller_, Sep 13 2011
%e A111192 a(2)=91 because the second sexy prime pair is (7, 13) and 7*13=91.
%t A111192 #(#+6)&/@Select[Prime[Range[100]], PrimeQ[#+6]&] (* _Harvey P. Dale_, Dec 17 2010 *)
%t A111192 (* For checking large numbers, the following code is better. For instance, we could use the fQ function to determine that 229031718473564142083 is not in this sequence. *) fQ[n_] := Block[{fi = FactorInteger[n]}, Last@# & /@ fi == {1, 1} && Differences[ First@# & /@ fi] == {6}]; Select[ Range[125000], fQ] (* _Robert G. Wilson v_, Feb 08 2012 *)
%t A111192 Select[Table[4 n^2 - 9, {n, 300}], PrimeOmega[#] == 2 &] (* _Vincenzo Librandi_, Jan 26 2016 *)
%o A111192 (Haskell)
%o A111192 a111192 n = a111192_list !! (n-1)
%o A111192 a111192_list = f a000040_list where
%o A111192    f (p:ps@(q:r:_)) | q - p == 6 = (p*q) : f ps
%o A111192                     | r - p == 6 = (p*r) : f ps
%o A111192                     | otherwise  = f ps
%o A111192 -- _Reinhard Zumkeller_, Sep 13 2011
%o A111192 (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [1..300] | IsSemiprime(s) where s is 4*n^2-9]; // _Vincenzo Librandi_, Jan 26 2016
%Y A111192 Cf. A023201, A104229.
%Y A111192 Cf. A037074, A143206, A195118; intersection of A143205 and A001358.
%K A111192 nonn
%O A111192 1,1
%A A111192 Shawn M Moore (sartak(AT)gmail.com), Oct 23 2005