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%I #11 Sep 06 2017 21:26:52
%S 2,3,1,8,6,12,5,4,10,16,18,15,24,9,36,7,25,14,42,21,20,32,28,40,48,64,
%T 35,72,27,30,45,80,63,49,81,88,50,90,60,54,70,99,100,96,110,11,108,22,
%U 120,33,56,44,130,55,117,84,66,144,140,156,77,168,104,180,121,192,13
%N Beginning with the sequence S(1)={1} form, in succession, the sequence S(n) for n=2,3,4,... by inserting the n smallest multiples of n that have not been used previously, in order of increasing size, n-1 of them between the final n terms of S(n-1) and the final multiple after the last term of S(n-1). {a(n)} is the limit of this process as n -> inf.
%C After n steps of the construction process n(n-1)/2 terms have been decided.
%H Ivan Neretin, <a href="/A096063/b096063.txt">Table of n, a(n) for n = 1..8001</a>
%e 1
%e 2,1,4 (multiples of 2 placed alternately )
%e 2,3,1,6,4,9,(multiples of 3 placed alternately )
%e 2,3,1,8,6,12,4,16,9,20
%e 2,3,1,8,6,12,5,4,10,16,15,9,25,20,30
%e The next step is to place unused multiples of 6, i.e. 18,24,36,42,48,54 at position marked ##:
%e 2,3,1,8,6,12,5,4,10,16,##,15,##,9,##,25,##,20,##,30,##
%e ...
%e After the 5th stage the terms 2,3,1,8,6,12,5,4,10,16 remain unchanged, hence form the initial 10 terms of the desired sequence.
%t mx = 13; a = {2, 1, 4}; Do[d = Complement[Range[Max[a] + 1]*n, a]; a = Join[Drop[a, -n], Riffle[Take[a, -n], Take[d, n]]], {n, 3, mx}]; Take[a, mx (mx - 1)/2] (* _Ivan Neretin_, Sep 06 2017 *)
%K nonn,look
%O 1,1
%A _Amarnath Murthy_, Jun 18 2004
%E Extended and edited by _John W. Layman_, Jun 06 2005
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