A111192 Product of the n-th sexy prime pair.

55, 91, 187, 247, 391, 667, 1147, 1591, 1927, 2491, 3127, 4087, 4891, 5767, 7387, 9991, 10807, 11227, 12091, 17947, 23707, 25591, 28891, 30967, 37627, 38407, 51067, 52891, 55687, 64507, 67591, 70747, 75067, 78391, 96091, 98587, 111547, 122491, 126727, 136891

Offset: 1

Author

Shawn M Moore (sartak(AT)gmail.com), Oct 23 2005

Keywords

• nonn

Comments

Semiprime of the form 4*m^2-9 = (2*m-3)*(2*m+3). - Vincenzo Librandi, Jan 26 2016

Examples

			a(2)=91 because the second sexy prime pair is (7, 13) and 7*13=91.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Sexy Primes. [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].

Crossrefs

Cf. A023201, A104229.

Cf. A037074, A143206, A195118; intersection of A143205 and A001358.

Programs

Haskell

a111192 n = a111192_list !! (n-1)
a111192_list = f a000040_list where
   f (p:ps@(q:r:_)) | q - p == 6 = (p*q) : f ps
                    | r - p == 6 = (p*r) : f ps
                    | otherwise  = f ps
-- Reinhard Zumkeller, Sep 13 2011

Magma

IsSemiprime:=func; [s: n in [1..300] | IsSemiprime(s) where s is 4*n^2-9]; // Vincenzo Librandi, Jan 26 2016

Mathematica

#(#+6)&/@Select[Prime[Range[100]], PrimeQ[#+6]&] (* Harvey P. Dale, Dec 17 2010 *)
(* 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 *)
Select[Table[4 n^2 - 9, {n, 300}], PrimeOmega[#] == 2 &] (* Vincenzo Librandi, Jan 26 2016 *)

Formula

a(n) = A023201(n) * A046117(n). - Reinhard Zumkeller, Sep 13 2011