A285200 a(n) = floor the elevator is on at the n-th stage of Ken Knowlton's elevator problem, version 1.

1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1

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, otherwise down.

See A285202 for an alternative way to display this sequence.

References

Ken Knowlton, Email to R. L. Graham, Apr 26 2017

Links

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

Ken Knowlton, Illustration showing what floor the elevator is on for the first 49 stages

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 then f:=f+1; else f:=f-1; fi;
hit[f]:=hit[f]+1; a:=[op(a), f];
if (hit[f] mod f) = 0 then dir:=1; else dir:=-1; fi;
od:
a;

Crossrefs

Cf. A285201, A285202, A285203.

See A286281 for a second version of the elevator problem.

Sequence in context: A066856 A089280 A246960 * A308567 A192099 A193101

Adjacent sequences: A285197 A285198 A285199 * A285201 A285202 A285203

Keyword

nonn

Author

N. J. A. Sloane, May 02 2017

Status

approved