%I A114112
%S A114112 1,2,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17,20,19,22,21,24,23,26,25,
%T A114112 28,27,30,29,32,31,34,33,36,35,38,37,40,39,42,41,44,43,46,45,48,47,50,
%U A114112 49,52,51,54,53,56,55,58,57,60,59,62,61,64,63,66,65,68,67,70,69,72,71
%N A114112 a(1)=1; for n>1, a(n) is the smallest positive integer not occurring 
               earlier in the sequence such that a(n) does not divide sum{k=1 to 
               n-1} a(k).
%H A114112 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A114112 a(1)=1. a(2)=2. For n>=3, a(n) = A014681(n) = A103889(n).
%t A114112 a[1] = 1; a[n_] := a[n] = Block[{k = 1, s, t = Table[ a[i], {i, n - 1}]}, 
               s = Plus @@ t; While[ Position[t, k] != {} || Mod[s, k] == 0, k++ 
               ]; k]; Array[a, 72] (* Robert G. Wilson v *)
%Y A114112 Cf. A014681, A103889, A114113.
%Y A114112 Sequence in context: A067747 A073846 A110458 this_sequence A113981 A143692 
               A114792
%Y A114112 Adjacent sequences: A114109 A114110 A114111 this_sequence A114113 A114114 
               A114115
%K A114112 easy,nonn
%O A114112 1,2
%A A114112 Leroy Quet Nov 13 2005
%E A114112 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 18 2005