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A006999
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Partitioning integers to avoid arithmetic progressions of length 3.
(Formerly M1047)
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17
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0, 1, 2, 4, 7, 11, 17, 26, 40, 61, 92, 139, 209, 314, 472, 709, 1064, 1597, 2396, 3595, 5393, 8090, 12136, 18205, 27308, 40963, 61445, 92168, 138253, 207380, 311071, 466607, 699911, 1049867, 1574801, 2362202, 3543304, 5314957, 7972436
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OFFSET
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0,3
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COMMENTS
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It appears that, aside from the first term, this is the (L)-sieve transform of A016789 ={2,5,8,11,...,3n+2....}. This has been verified up to a(30)=311071. See A152009 for the definition of the (L)-sieve transform. - John W. Layman, Nov 20 2008
a(n) is also the largest-index square reachable in n jumps if we start at square 0 of the Infinite Sidewalk. - Jose Villegas, Mar 27 2023
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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D. R. Hofstadter, Eta-Lore [Cached copy, with permission]
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FORMULA
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a(n) = floor((3a(n-1)+2)/2).
a(n) = -1 + floor(c*(3/2)^n) where c=1.081513668589844877304633988599549408710737041542024954790295591585622666484989650922411026555488940... - Benoit Cloitre, Jan 10 2002
a(n+1) = (3*a(n))/2+1 if a(n) is even. a(n+1) = (3*a(n)+1)/2 if a(n) is odd. - Miquel Cerda, Jun 15 2019
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MATHEMATICA
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a[0] = 0; a[n_] := a[n] = Floor[(3 a[n-1] + 2)/2];
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PROG
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(PARI) a(n)=if(n<1, 0, floor((3*a(n-1)+2)/2))
(Haskell)
a006999 n = a006999_list !! n
a006999_list = 0 : map ((`div` 2) . (+ 2) . (* 3)) a006999_list
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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