OFFSET
0,2
COMMENTS
This is a permutation of the natural numbers.
For n > 2: a(n) is prime iff a(n) < a(n-1); a(A112988(n)) = A000040(n); inverse: A112990. - Reinhard Zumkeller, Oct 08 2005
For n > 3, a(n) can be described as follows: all composite numbers in natural order, with primes inserted so that every prime p immediately follows 2p. - Ivan Neretin, Apr 26 2015
LINKS
MATHEMATICA
A089088 = {a[0] = 1, a[1] = 2}; a[n_] := Catch[For[k = Min[ Complement[ Range[Max[A089088] + 1], A089088]], True, k++, If[ !MemberQ[A089088, k] && Or @@ (GCD[k, #] > 1&) /@ A089088, AppendTo[A089088, k]; Throw[k]]]]; Table[a[n], {n, 0, 88}] (* Jean-François Alcover, Jul 18 2012 *)
Nest[Append[#1, Block[{k = 1}, While[Nand[FreeQ[#1, k], AnyTrue[#1, ! CoprimeQ[#, k] &]], k++]; k]] &, {1, 2}, 87] (* Michael De Vlieger, Nov 18 2017 *)
PROG
(Haskell)
import Data.List (delete)
a089088 n = a089088_list !! n
a089088_list = 1 : 2 : f [3..] [1, 2] where
f xs ys = y : f (delete y xs) (y : ys) where
y = head $ filter (\z -> any (> 1) $ map (gcd z) ys) xs
-- Reinhard Zumkeller, Feb 27 2013
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Leroy Quet, Dec 04 2003
EXTENSIONS
More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Jun 16 2004
STATUS
approved