A286281 a(n) = floor the elevator is on at the n-th stage of Ken Knowlton's elevator problem, version 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, 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, 1, 2, 3, 4, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 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

Offset

1,2

Comments

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.

References

Ken Knowlton, Email to R. L. Graham and N. J. A. Sloane, May 04 2017

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Ken Knowlton, Illustration of initial terms showing floors the two versions of the elevator are on. Top: version 1 (A285200), bottom: version 2 (A286281)

Maple

hit:=Array(1..50, 0);
hit[1]:=1; a:=[1]; dir:=1; f:=1;
for s from 2 to 1000 do
if dir>0 or f=1 then f:=f+1; hit[f]:=hit[f]+1; dir:=1; else f:=f-1; dir:=-1; fi;
a:=[op(a), f];
if (dir=1) and ((hit[f] mod f) = 0) then dir:=1; else dir:=-1; fi;
od:
a;

Mathematica

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 *)

Crossrefs

For records see A286282.

See A285200 for the first version of the elevator problem.

Sequence in context: A277889 A018194 A338630 * A229830 A105203 A317952

Adjacent sequences: A286278 A286279 A286280 * A286282 A286283 A286284

Keyword

nonn

Author

N. J. A. Sloane, May 09 2017

Status

approved