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A109636
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Let T(n,k) be the n-th k-almost prime. Then a(n) = T(n,k) such that k is minimal and for all l>0, T(n,k+l) > 2^l * T(n,k).
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1
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2, 3, 9, 10, 27, 28, 30, 81, 84, 88, 90, 100, 104, 243, 252, 264, 270, 272, 280, 300, 304, 312, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040, 2187, 2208, 2268, 2352, 2368, 2376, 2430, 2448, 2464, 2520, 2624
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OFFSET
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1,1
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COMMENTS
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If one writes the k-almost primes in rows (one row for each k), one observes that there exists a P_{k_0}(n) such that P_{k_0+1}(n) = 2P_{k_0}(n) and for each k>=k_0, P_{k+1}(n)=2P_{k}(n). Then a(n) = P_{k_0}(n). In other words in the columns the values double from row k_0 on. - Peter Pein (petsie(AT)dordos.net), Mar 16 2007
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LINKS
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MATHEMATICA
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a[n_] := Module[{p = Prime[Range[n]], pal}, pal = Transpose /@ Partition[NestList[Take[Union[Flatten[Outer[Times, #1, p]]], Length[#1]] &, p, n], 2, 1]; Complement @@ Transpose[Cases[pal, {k_, kk_} /; kk == 2*k, {2}]]] ; a[50] (* Peter Pein, Nov 10 2007 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Yury V. Shlapak (shlapak(AT)imp.kiev.ua), Aug 04 2005
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EXTENSIONS
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More terms from Peter Pein, Mar 16 2007
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STATUS
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approved
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