A074480 Multiplicative closure of twin prime pair products (A037074).

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

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. A037074, A001359, A006512, A062505.

Cf. A071700 (subsequence).

Sequence in context: A142591 A321617 A254031 * A194580 A210503 A037074

Adjacent sequences: A074477 A074478 A074479 * A074481 A074482 A074483

Keyword

nonn,nice

Author

Reinhard Zumkeller, Aug 23 2002

Status

approved