%I A096063
%S A096063 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 A096063 35,72,27,30,45,80,63,49,81,88,50,90,60,54,70,99,100,96,110,11,108,22,
%U A096063 120,33,56,44,130,55,117,84,66,144,140,156,77,168,104,180,121,192,13
%N A096063 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 A096063 After n steps of the construction process n(n-1)/2 terms have been decided.
%e A096063 1
%e A096063 2,1,4 (multiples of 2 placed alternately )
%e A096063 2,3,1,6,4,9,(multiples of 3 placed alternately )
%e A096063 2,3,1,8,6,12,4,16,9,20
%e A096063 2,3,1,8,6,12,5,4,10,16,15,9,25,20,30
%e A096063 The next step is to place unused multiples of 6, i.e. 18,24,36,42,48,
               54 at position marked ##:
%e A096063 2,3,1,8,6,12,5,4,10,16,##,15,##,9,##,25,##,20,##,30,##
%e A096063 ...
%e A096063 After the 5-th 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.
%Y A096063 Sequence in context: A147865 A011152 A078298 this_sequence A101281 A106033 
               A121634
%Y A096063 Adjacent sequences: A096060 A096061 A096062 this_sequence A096064 A096065 
               A096066
%K A096063 nonn
%O A096063 1,1
%A A096063 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 18 2004
%E A096063 Extended and edited by John W. Layman (layman(AT)math.vt.edu), Jun 06 
               2005