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%I #19 May 10 2017 14:30:22
%S 1,2,1,2,3,2,1,2,1,2,3,2,1,2,1,2,3,4,3,2,1,2,1,2,3,2,1,2,1,2,3,2,1,2,
%T 1,2,3,4,3,2,1,2,1,2,3,2,1,2,1,2,3,2,1,2,1,2,3,4,3,2,1,2,1,2,3,2,1,2,
%U 1,2,3,2,1,2,1,2,3,4,5,4,3,2,1,2,1,2,3,2,1,2,1,2,3,2,1,2,1,2,3,4
%N a(n) = floor the elevator is on at the n-th stage of Ken Knowlton's elevator problem, version 2.
%C An elevator steps up or down a floor at a time. It starts at floor 1, and always goes up from floor 1. From each floor m, it steps up every m-th time it stops there (except that stops when the elevator is going down don't count), otherwise down.
%D Ken Knowlton, Email to R. L. Graham and N. J. A. Sloane, May 04 2017
%H N. J. A. Sloane, <a href="/A286281/b286281.txt">Table of n, a(n) for n = 1..20000</a>
%H Ken Knowlton, <a href="/A286281/a286281.pdf">Illustration of initial terms showing floors the two versions of the elevator are on. Top: version 1 (A285200), bottom: version 2 (A286281) </a>
%p hit:=Array(1..50, 0);
%p hit[1]:=1; a:=[1]; dir:=1; f:=1;
%p for s from 2 to 1000 do
%p if dir>0 or f=1 then f:=f+1; hit[f]:=hit[f]+1; dir:=1; else f:=f-1; dir:=-1; fi;
%p a:=[op(a), f];
%p if (dir=1) and ((hit[f] mod f) = 0) then dir:=1; else dir:=-1; fi;
%p od:
%p a;
%t f[n_, m_: 20] := Block[{a = {}, r = ConstantArray[0, m], f = 1, d = 0}, Do[AppendTo[a, f]; If[d == 1, r = MapAt[# + 1 &, r, f]]; If[Or[And[ Divisible[r[[f]], f], d == 1], f == 1], f++; d = 1, f--; d = -1], {i, n}]; a]; f@ 100 (* _Michael De Vlieger_, May 10 2017 *)
%Y For records see A286282.
%Y See A285200 for the first version of the elevator problem.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, May 09 2017
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