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A007448
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Knuth's sequence (or Knuth numbers): a(n+1) = 1 + min ( 2 a[ n/2 ], 3 a[ n/3 ] ).
(Formerly M2276)
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7
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1, 3, 3, 4, 7, 7, 7, 9, 9, 10, 13, 13, 13, 15, 15, 19, 19, 19, 19, 21, 21, 22, 27, 27, 27, 27, 27, 28, 31, 31, 31, 39, 39, 39, 39, 39, 39, 39, 39, 40, 43, 43, 43, 45, 45, 46, 55, 55, 55, 55, 55, 55, 55, 55, 55, 57, 57, 58, 63, 63, 63, 63, 63, 64, 67, 67, 67, 79, 79, 79, 79
(list;
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OFFSET
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0,2
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COMMENTS
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Record values and where they occur: a(A002977(n-1))=A002977(n) and a(m)<A002977(n) for m<A002977(n-1). [From Reinhard Zumkeller, Jul 13 2010]
A003817 and A179526 are subsequences. [From Reinhard Zumkeller, Jul 18 2010]
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 78.
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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T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Knuth Number.
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = 1 + Min[ 2a[Ceiling[(n - 1)/2]], 3a[Ceiling[(n - 1)/3]]]; Table[ a[n], {n, 72}] (from Robert G. Wilson v Jan 29 2005)
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PROG
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(Haskell)
a007448 n = a007448_list !! n
a007448_list = f [0] [0] where
f (x:xs) (y:ys) = z : f (xs ++ [2*z, 2*z]) (ys ++ [3*z, 3*z, 3*z])
where z = 1 + min x y
-- Reinhard Zumkeller, Sep 20 2011
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CROSSREFS
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Cf. A002977.
Sequence in context: A059871 A076619 A216626 * A155689 A051263 A058674
Adjacent sequences: A007445 A007446 A007447 * A007449 A007450 A007451
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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