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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for sequences that are permutations of the natural numbers

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-Fran├žois 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: A236675 A210771 A115316 * A251622 A073899 A232846

Adjacent sequences:  A089085 A089086 A089087 * A089089 A089090 A089091

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

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Last modified August 8 21:18 EDT 2022. Contains 356016 sequences. (Running on oeis4.)