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A074480
Multiplicative closure of twin prime pair products (A037074).
6
1, 15, 35, 143, 225, 323, 525, 899, 1225, 1763, 2145, 3375, 3599, 4845, 5005, 5183, 7875, 10403, 11305, 11663, 13485, 18375, 19043, 20449, 22499, 26445, 31465, 32175, 32399, 36863, 39203, 42875, 46189, 50625, 51983, 53985, 57599, 61705
OFFSET
1,2
COMMENTS
A072965(a(n)) = 1.
LINKS
EXAMPLE
a(99)=1040399=1019*1021; a(101)=1090125=(3*5)*(3*5)*(3*5)*(17*19); a(103)=1101275=(5*7)*(5*7)*(29*31); a(105)=1126125= (3*5)*(3*5)*(5*7)*(11*13).
MATHEMATICA
max = 70000; t1 = Select[Prime /@ Range[PrimePi[Sqrt[max]]], PrimeQ[# + 2] &]; pairs = Join[{1}, t1*(t1 + 2)]; f[pairs_] := Outer[Times, pairs, pairs] // Flatten // Union // Select[#, # <= max &] &; FixedPoint[f, pairs] (* Jean-François Alcover, Dec 11 2012 *)
PROG
(Haskell)
import Data.Set (Set, singleton, delete, findMin, deleteFindMin, insert)
a074480 n = a074480_list !! (n-1)
a074480_list = multClosure a037074_list where
multClosure [] = [1]
multClosure (b:bs) = 1:h [b] (singleton b) bs where
h cs s [] = m:h (m:cs) (foldl (flip insert) s' $ map (*m) cs) []
where (m, s') = deleteFindMin s
h cs s xs'@(x:xs)
| m < x = m:h (m:cs) (foldl (flip insert) s' $ map (*m) cs) xs'
| otherwise = x:h (x:cs) (foldl (flip insert) s $ map (*x) (x:cs)) xs
where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Aug 14 2011
CROSSREFS
Cf. A071700 (subsequence).
Sequence in context: A142591 A321617 A254031 * A194580 A210503 A037074
KEYWORD
nonn,nice
AUTHOR
Reinhard Zumkeller, Aug 23 2002
STATUS
approved