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A265577 LCM-transform of Yellowstone permutation A098550.

%I A265577 #13 Dec 03 2017 17:16:15
%S A265577 1,2,3,2,3,2,5,7,1,1,5,1,1,2,1,1,1,1,3,11,13,1,1,1,1,1,1,17,2,1,1,1,1,
%T A265577 1,1,1,1,1,1,7,19,1,1,1,1,1,1,1,23,1,1,1,1,1,1,1,3,1,29,31,1,1,1,1,2,
%U A265577 1,1,1,1,1,1
%N A265577 LCM-transform of Yellowstone permutation A098550.
%H A265577 A. Nowicki, <a href="http://arxiv.org/abs/1310.2416">Strong divisibility and LCM-sequences</a>, arXiv:1310.2416 [math.NT], 2013.
%H A265577 A. Nowicki, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.122.10.958">Strong divisibility and LCM-sequences</a>, Am. Math. Mnthly 122 (2015), 958-966.
%p A265577 LCMXfm:=proc(a) local L,i,n,g,b;
%p A265577 L:=nops(a);
%p A265577 g:=Array(1..L,0); b:=Array(1..L,0);
%p A265577 b[1]:=a[1]; g[1]:=a[1];
%p A265577 for n from 2 to L do g[n]:=ilcm(g[n-1],a[n]); b[n]:=g[n]/g[n-1]; od;
%p A265577 lprint([seq(b[i],i=1..L)]);
%p A265577 end;
%p A265577 # let t1 contain the first 100 terms of A098550
%p A265577 LCMXfm(t1);
%t A265577 LCMXfm[a_List] := Module[{L = Length[a], b, g}, b[1] = g[1] = a[[1]]; b[_] = 0; g[_] = 0; Do[g[n] = LCM[g[n-1], a[[n]]]; b[n] = g[n]/g[n-1], {n, 2, L}]; Array[b, L]];
%t A265577 y[n_ /; n <= 3] := n; y[n_] := y[n] = For[k = 1, True, k++, If[ FreeQ[ Array[y, n-1], k], If[GCD[k, y[n-1]] == 1 && GCD[k, y[n-2]] > 1, Return[k]]]];
%t A265577 Yperm = Array[y, 100];
%t A265577 LCMXfm[Yperm] (* _Jean-François Alcover_, Dec 03 2017 *)
%Y A265577 Cf. A064413.
%Y A265577 Other LCM-transforms are A061446, A265574, A265575, A265576.
%K A265577 nonn
%O A265577 1,2
%A A265577 _N. J. A. Sloane_, Jan 02 2016