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A111192
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Product of the n-th sexy prime pair.
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9
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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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].
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FORMULA
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EXAMPLE
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a(2)=91 because the second sexy prime pair is (7, 13) and 7*13=91.
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MATHEMATICA
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#(#+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 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Shawn M Moore (sartak(AT)gmail.com), Oct 23 2005
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STATUS
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approved
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