[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
login
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
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
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
(Python)
def aupton(nn):
alst = [1]
[alst.append(1 + min(2*alst[n//2], 3*alst[n//3])) for n in range(nn)]
return alst
print(aupton(70)) # Michael S. Branicky, Mar 28 2022
CROSSREFS
Cf. A002977.
Sequence in context: A216626 A319526 A258835 * A155689 A051263 A378248
KEYWORD
easy,nonn,nice,changed
STATUS
approved