A089088 - OEIS

%I #28 Nov 19 2017 01:38:47

%S 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,

%T 32,33,34,17,35,36,38,19,39,40,42,44,45,46,23,48,49,50,51,52,54,55,56,

%U 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

%N 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.

%C This is a permutation of the natural numbers.

%C 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

%C 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

%H Reinhard Zumkeller, <a href="/A089088/b089088.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%t 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 *)

%t 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 *)

%o (Haskell)

%o import Data.List (delete)

%o a089088 n = a089088_list !! n

%o a089088_list = 1 : 2 : f [3..] [1,2] where

%o   f xs ys = y : f (delete y xs) (y : ys) where

%o     y = head $ filter (\z -> any (> 1) $ map (gcd z) ys) xs

%o -- _Reinhard Zumkeller_, Feb 27 2013

%Y Cf. A064413.

%Y Cf. A112975.

%K nonn,nice,easy

%O 0,2

%A _Leroy Quet_, Dec 04 2003

%E More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Jun 16 2004