%I
%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
