%I #12 Feb 18 2017 22:01:34

%S 1,2,2,3,5,4,4,8,8,7,9,10,10,14,14,10,11,17,18,15,19,16,14,23,24,17,

%T 19,27,18,23,25,20,20,30,30,19,27,24,20,31,39,32,30,38,38,24,24,34,34,

%U 50,46,31,39,53,54,47,49,40,38,59,58,57,62,58,48,49,57,39

%N a(n) is the largest step size that is taken 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.

%H Peter Kagey, <a href="/A282443/b282443.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A282442(n) - 1.

%e For n = 4:

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

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

%e step size 3: 0 -> 3.

%e Because the walker cannot take four steps down, the biggest step size is 3.

%e Therefore a(4) = 3.

%Y Cf. A282442, A282444.

%K nonn

%O 1,2

%A _Peter Kagey_, Feb 15 2017