A265577 - OEIS

%I #13 Dec 03 2017 17:16:15

%S 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 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 1,1,1,1,1,1

%N LCM-transform of Yellowstone permutation A098550.

%H A. Nowicki, <a href="http://arxiv.org/abs/1310.2416">Strong divisibility and LCM-sequences</a>, arXiv:1310.2416 [math.NT], 2013.

%H 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 LCMXfm:=proc(a) local L,i,n,g,b;

%p L:=nops(a);

%p g:=Array(1..L,0); b:=Array(1..L,0);

%p b[1]:=a[1]; g[1]:=a[1];

%p for n from 2 to L do g[n]:=ilcm(g[n-1],a[n]); b[n]:=g[n]/g[n-1]; od;

%p lprint([seq(b[i],i=1..L)]);

%p end;

%p # let t1 contain the first 100 terms of A098550

%p LCMXfm(t1);

%t 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 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 Yperm = Array[y, 100];

%t LCMXfm[Yperm] (* _Jean-François Alcover_, Dec 03 2017 *)

%Y Cf. A064413.

%Y Other LCM-transforms are A061446, A265574, A265575, A265576.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jan 02 2016