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 A098548 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). 21
 1, 2, 3, 4, 9, 10, 21, 22, 27, 28, 33, 34, 39, 40, 51, 52, 57, 58, 63, 64, 69, 70, 81, 82, 87, 88, 93, 94, 99, 100, 111, 112, 117, 118, 123, 124, 129, 130, 141, 142, 147, 148, 153, 154, 159, 160, 171, 172, 177, 178, 183, 184, 189, 190, 201, 202, 207, 208, 213, 214 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 A098549(n) = a(a(n)). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015 and J. Int. Seq. 18 (2015) 15.6.7. Reinhard Zumkeller, Table of n, a(n) for n = 1..100000 MAPLE 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 MATHEMATICA 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 *) PROG (Haskell) a098548 n = a098548_list !! (n-1) a098548_list = 1 : 2 : 3 : f 2 3 [4..] where    f u v (w:ws) = if gcd u w > 1 && gcd v w == 1                      then w : f v w ws else f u v ws -- Reinhard Zumkeller, Nov 21 2014 CROSSREFS Cf. A098549, A098550. 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). Cf. also A251535 and A251536 (bisections), A251537, A251538, A251539 (jumps), A251540. Sequence in context: A174437 A127150 A256189 * A076963 A081871 A329573 Adjacent sequences:  A098545 A098546 A098547 * A098549 A098550 A098551 KEYWORD nonn AUTHOR Reinhard Zumkeller, Sep 14 2004 STATUS approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)