OFFSET
1,1
COMMENTS
All terms are 3-smooth. - Reinhard Zumkeller, Aug 13 2015
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
REFERENCES
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).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Rémy Sigrist, Scatterplot of the 2-adic valuation of a(n) vs the 3-adic valuation of a(n) for n = 1..50000
Robert G. Wilson v, Note, n.d.
FORMULA
Conjecture: Sum_{n>=1} 1/a(n) = 181/144. - Amiram Eldar, Jul 31 2022
MATHEMATICA
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 *)
PROG
(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
-- Reinhard Zumkeller, Aug 13 2015
(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
MUList(41) |> println # Peter Luschny, Apr 07 2019
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved