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 A251622 a(1) = 1; a(2) = 2; for n > 2, a(n) = smallest number not already used which shares a factor with a(n-1) or a(n-2). 10
 1, 2, 4, 6, 3, 8, 9, 10, 5, 12, 14, 7, 16, 18, 15, 20, 21, 22, 11, 24, 26, 13, 28, 30, 25, 27, 33, 36, 32, 34, 17, 38, 19, 40, 35, 42, 39, 44, 45, 46, 23, 48, 50, 51, 52, 54, 56, 49, 58, 29, 60, 55, 57, 63, 66, 62, 31, 64, 68, 70, 65, 72, 69, 74, 37, 76, 78, 75, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This appears certainly to be a permutation of the positive integers. I believe the arguments we used to show that the EKG sequence (A064413) is a permutation of the natural numbers apply here with almost no change. - N. J. A. Sloane, Jan 02 2015 For n > 2: gcd(a(n),a(n-1)*a(n-2)) > 1. - Reinhard Zumkeller, Apr 05 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446. J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG Sequence MATHEMATICA a = 1; a = 2; a[n_] := a[n] = For[k = 1, True, k++, If[FreeQ[Array[a, n-1], k], If[!CoprimeQ[k, a[n-1]] || !CoprimeQ[k, a[n-2]], Return[k]]]]; Array[a, 100] (* Jean-François Alcover, Sep 05 2018 *) PROG (PARI) invecn(v, k, x)=for(i=1, k, if(v[i]==x, return(i))); 0 alist(n)=local(v=vector(n), x); v=1; v=2; for(k=3, n, x=3; while(invecn(v, k-1, x)||(gcd(v[k-1], x)==1&&gcd(v[k-2], x)==1), x++); v[k]=x); v (Haskell) a251622 n = a251622_list !! (n-1) a251622_list = 1 : 2 : f 1 2 [3..] where    f u v xs = g xs where      g (w:ws) = if gcd w u > 1 || gcd w v > 1                    then w : f v w (delete w xs) else g ws -- Reinhard Zumkeller, Apr 05 2015 CROSSREFS Cf. A064413, A089088, A098550. Cf. A256628 (conjectured inverse). Sequence in context: A210771 A115316 A089088 * A073899 A232846 A101543 Adjacent sequences:  A251619 A251620 A251621 * A251623 A251624 A251625 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Dec 06 2014 STATUS approved

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Last modified August 10 09:58 EDT 2022. Contains 356039 sequences. (Running on oeis4.)