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A282442 a(n) is the smallest step size that does not occur on a staircase of n steps when following the following procedure: Take steps of length 1 up a staircase until you can't step any further, then take steps of length 2 down until you can't step any further, and so on. 8
2, 3, 3, 4, 6, 5, 5, 9, 9, 8, 10, 11, 11, 15, 15, 11, 12, 18, 19, 16, 20, 17, 15, 24, 25, 18, 20, 28, 19, 24, 26, 21, 21, 31, 31, 20, 28, 25, 21, 32, 40, 33, 31, 39, 39, 25, 25, 35, 35, 51, 47, 32, 40, 54, 55, 48, 50, 41, 39, 60, 59, 58, 63, 59, 49, 50, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) <= n + 1.

From the Mathematics Stack Exchange question:

Assume there are n stairs (so n+1 places to stand).

Starting from the bottom, go up 1 stair at a time, until you reach the top;

then turn around and go down 2 stairs at a time, until you can't go further;

then turn around and go up 3 stairs at a time, until you can't go further;

then 4, 5, 6, etc. stairs at a time, until you can't even make one step.

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000

Sheljohn, A curious sequence, Mathematics Stack Exchange, Feb 15 2017

EXAMPLE

For n = 4:

step size 1: 0 -> 1 -> 2 -> 3 -> 4;

step size 2: 4 -> 2 -> 0;

step size 3: 0 -> 3.

Because the walker cannot take four steps down, a(4) = 4.

MAPLE

A282442 := proc(n)

    local h, dir, ss, ns;

    h := 0 ;

    dir := 1 ;

    for ss from 1 do

        if dir > 0 then

            ns := floor((n-h)/ss) ;

        else

            ns := floor(h/ss) ;

        end if;

        if ns = 0 then

            return ss;

        end if;

        h := h+dir*ns*ss ;

        dir := -dir ;

    end do:

end proc:

seq(A282442(n), n=1..100) ; # R. J. Mathar, Feb 25 2017

CROSSREFS

Sequence in context: A159999 A003977 A003971 * A200668 A200469 A200251

Adjacent sequences:  A282439 A282440 A282441 * A282443 A282444 A282445

KEYWORD

nonn,look

AUTHOR

Peter Kagey, Feb 15 2017

STATUS

approved

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)