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A007335
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MU-numbers: next term is uniquely the product of 2 earlier terms.
(Formerly M0794)
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5
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2, 3, 6, 12, 18, 24, 48, 54, 96, 162, 192, 216, 384, 486, 768, 864, 1458, 1536, 1944, 3072, 3456, 4374, 6144, 7776, 12288, 13122, 13824, 17496, 24576, 31104, 39366, 49152, 55296, 69984, 98304, 118098, 124416, 157464, 196608, 221184, 279936
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OFFSET
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1,1
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COMMENTS
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Empirically, this sequence corresponds to numbers of the form 2^v * 3^w with v = 1 or w = 1 or v and w both odd (see illustration in Links section). - Rémy Sigrist, Feb 16 2023
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REFERENCES
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Clifford A. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 359.
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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FORMULA
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Conjecture: Sum_{n>=1} 1/a(n) = 181/144. - Amiram Eldar, Jul 31 2022
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MATHEMATICA
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s={2, 3}; Do[n=Select[ Table[s[[j]] s[[k]], {j, Length@s}, {k, j+1, Length@s}] // Flatten // Sort // Split, #[[1]] > s[[-1]] && Length[#] == 1 &][[1, 1]]; AppendTo[s, n], {39}]; s (* Jean-François Alcover, Apr 22 2011 *)
Nest[Append[#, SelectFirst[Union@ Select[Tally@ Map[Times @@ # &, Select[Permutations[#, {2}], #1 < #2 & @@ # &]], Last@ # == 1 &][[All, 1]], Function[k, FreeQ[#, k]]]] &, {2, 3}, 39] (* Michael De Vlieger, Nov 16 2017 *)
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PROG
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(Haskell)
a007335 n = a007335_list !! (n-1)
a007335_list = 2 : 3 : f [3, 2] (singleton 6 1) where
f xs m | v == 1 = y : f (y : xs) (g (map (y *) xs) m')
| otherwise = f xs m'
where g [] m = m
g (z:zs) m = g zs $ insertWith (+) z 1 m
((y, v), m') = deleteFindMin m
(Julia)
function isMU(u, n, h, i, r)
ur = u[r]; ui = u[i]
ur <= ui && return h
if ur * ui > n
r -= 1
elseif ur * ui < n
i += 1
else
h && return false
h = true; i += 1; r -= 1
end
isMU(u, n, h, i, r)
end
function MUList(len)
u = Array{Int, 1}(undef, len)
u[1] = 2; u[2] = 3; i = 2; n = 2
while i < len
n += 1
if isMU(u, n, false, 1, i)
i += 1
u[i] = n
end
end
return u
end
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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