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A007448 Knuth's sequence (or Knuth numbers): a(n+1) = 1 + min( 2*a(floor(n/2)), 3*a(floor(n/3)) ).
(Formerly M2276)
8
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; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Record values and where they occur: a(A002977(n-1))=A002977(n) and a(m)<A002977(n) for m<A002977(n-1). - Reinhard Zumkeller, Jul 13 2010

A003817 and A179526 are subsequences. - Reinhard Zumkeller, Jul 18 2010

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Knuth Number.

MATHEMATICA

a[1] = 1; a[n_] := a[n] = 1 + Min[ 2a[Ceiling[(n - 1)/2]], 3a[Ceiling[(n - 1)/3]]]; Table[ a[n], {n, 72}] (* Robert G. Wilson v, Jan 29 2005 *)

PROG

(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

CROSSREFS

Cf. A002977.

Sequence in context: A266025 A216626 A258835 * A155689 A051263 A058674

Adjacent sequences:  A007445 A007446 A007447 * A007449 A007450 A007451

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)