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A089088
a(0) = 1, a(1) = 2; for n > 1, a(n) = smallest positive number not already in sequence which has GCD > 1 with some earlier term.
14
1, 2, 4, 6, 3, 8, 9, 10, 5, 12, 14, 7, 15, 16, 18, 20, 21, 22, 11, 24, 25, 26, 13, 27, 28, 30, 32, 33, 34, 17, 35, 36, 38, 19, 39, 40, 42, 44, 45, 46, 23, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 29, 60, 62, 31, 63, 64, 65, 66, 68, 69, 70, 72, 74, 37, 75, 76, 77, 78, 80, 81, 82, 41, 84, 85, 86, 43, 87, 88, 90, 91, 92, 93, 94, 47, 95, 96, 98, 99
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
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
Cf. A064413.
Cf. A112975.
Sequence in context: A359535 A115316 A375327 * A251622 A073899 A232846
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