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%I #11 May 13 2015 12:38:48
%S 1,3,7,12,18,10,19,30,17,31,16,36,57,35,58,34,59,33,60,32,61,98,136,
%T 97,137,96,54
%N a(1)=1. Given a(1),...,a(n-1), to find a(n), let S = {a(1), ..., a(n-1), |a(2)-a(1)|, ..., |a(n-1)-a(n-2)|}. Let d be the smallest positive integer not in S. Then a(n) is the smallest one of a(n-1)-d and a(n-1)+d which is a positive integer not in S union {d}.
%e For n=5, S={1,3,7,12, 2,4,5} so d=6. a(4)-d=6 is in S union {6}, so we have a(5)=a(4)+d=18.
%e a(28) does not exist: d=43, but both a(28)-43=11 and a(28)+43=97 are in S union {43}.
%t mex1[s_]:=Module[{n}, For[n=1, MemberQ[s, n], n++, Null]; n]; a[1]=1; a[n_]:=a[n]=Module[{as, d}, as=a/@Range[n-1]; as=Union[as, Abs[Drop[as, 1]-Drop[as, -1]]]; AppendTo[as, d=mex1[as]]; If[a[n-1]-d>0&&!MemberQ[as, a[n-1]-d], a[n-1]-d, If[ !MemberQ[as, a[n-1]+d], a[n-1]+d], False]]
%Y Cf. A005228.
%K nonn,fini,full
%O 1,2
%A _Dean Hickerson_, following a suggestion of _Leroy Quet_, May 28 2004
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