A098548 - OEIS

%I #45 Nov 27 2019 08:33:01

%S 1,2,3,4,9,10,21,22,27,28,33,34,39,40,51,52,57,58,63,64,69,70,81,82,

%T 87,88,93,94,99,100,111,112,117,118,123,124,129,130,141,142,147,148,

%U 153,154,159,160,171,172,177,178,183,184,189,190,201,202,207,208,213,214

%N a(n) = n if n <= 3, otherwise the smallest number > a(n-1) having at least one common factor with a(n-2) but none with a(n-1).

%C The number a(n) is even if and only if n is even. If n>=1, then a(2n) = a(2n-1) + 1. If n>=2, then a(2n+1) - a(2n) >= 5. As a consequence, if n>=15, then a(n) > 3n. - _Benoit Jubin_, Dec 07 2014

%C A098549(n) = a(a(n)).

%H Reinhard Zumkeller, <a href="/A098548/b098548.txt">Table of n, a(n) for n = 1..10000</a>

%H David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, <a href="http://arxiv.org/abs/1501.01669">The Yellowstone Permutation</a>, arXiv preprint arXiv:1501.01669 [math.NT], 2015 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.

%H Reinhard Zumkeller, <a href="/A098548/a098548.txt">Table of n, a(n) for n = 1..100000</a>

%p x2 := 0: for n from 1 to 1000 do x := x2 + 1: while (n >= 4 and (gcd(x,x2) > 1 or gcd(x,x1) = 1)) do x := x + 1: end do; print (n, x); x1 := x2: x2 := x: end do: # _David Applegate_, Nov 26 2014

%t a := {1, 2, 3}; For[n = 4, n <= 1000, n++, If[GCD[n, a[[-1]]] == 1 && GCD[n, a[[-2]]] > 1, AppendTo[a, n]]]; a (* _L. Edson Jeffery_, Dec 04 2014 *)

%o (Haskell)

%o a098548 n = a098548_list !! (n-1)

%o a098548_list = 1 : 2 : 3 : f 2 3 [4..] where

%o    f u v (w:ws) = if gcd u w > 1 && gcd v w == 1

%o                      then w : f v w ws else f u v ws

%o -- _Reinhard Zumkeller_, Nov 21 2014

%Y Cf. A098549, A098550.

%Y Cf. A158478 (smallest prime factor), A251104 (largest prime factor), A251139 (number of distinct prime factors), A251141 (total number of prime factors), A251046 (squarefree part), A251090 (squarefree kernel).

%Y Cf. also A251535 and A251536 (bisections), A251537, A251538, A251539 (jumps), A251540.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Sep 14 2004