Search: id:A113966
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%I A113966
%S A113966 1,3,5,2,6,10,4,7,9,11,8,13,15,17,12,19,14,18,22,16,21,23,20,26,29,24,
%T A113966 31,25,27,32,35,33,28,34,30,37,39,41,36,43,38,42,46,40,47,44,49,45,51,
%U A113966 53,48,55,52,57,50,54,58,61,56,59,62,65,63,67,60,68,71,64,69,73,66,70
%N A113966 a(1)=1; for n>1, a(n) is the smallest positive integer not occurring 
               earlier in the sequence such that |a(n)-a(n-1)| does not divide a(n).
%C A113966 Sequence is a permutation of the positive integers.
%C A113966 Proof that every number must eventually appear: Suppose not, let k be 
               smallest number that never appears. Then for every a(n-1) > k, we 
               have a(n-1)-k | k, i.e. i(a(n-1)-k) = k for some i with 1 <= i <= 
               k. Therefore a(n-1) <= (k+ik)/k <= k(k+1). So once a(n-1) > k(k+1), 
               we will have a(n) = k, a contradiction. - N. J. A. Sloane (njas(AT)research.att.com), 
               Jan 29 2006
%H A113966 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A113966 Among those positive integers not among the first 4 integers of the sequence, 
               a(5) = 6 is the smallest such that |a(5)-a(4)| = |6-2| = 4 does not 
               divide a(5) =6. 4, for example, is not among the first 4 terms of 
               the sequence, but |4-2| = 2 does divide 4. So a(5) is not 4, but 
               is instead 6.
%t A113966 f[l_] := Block[{k=1}, While[MemberQ[l, k] || Mod[k, Abs[k - Last[l]]] 
               == 0, k++ ]; Return[Append[l, k]]; ]; Nest[f, {1}, 100] (*Chandler*)
%Y A113966 Cf. A113963, A113967.
%Y A113966 Sequence in context: A010782 A139584 A064790 this_sequence A164611 A073897 
               A097465
%Y A113966 Adjacent sequences: A113963 A113964 A113965 this_sequence A113967 A113968 
               A113969
%K A113966 nonn,nice
%O A113966 1,2
%A A113966 Leroy Quet Nov 10 2005
%E A113966 Extended by Jim Nastos (nastos(AT)gmail.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), 
               Nov 13 2005

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