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A282443 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.

%I A282443 #12 Feb 18 2017 22:01:34
%S A282443 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 A282443 19,27,18,23,25,20,20,30,30,19,27,24,20,31,39,32,30,38,38,24,24,34,34,
%U A282443 50,46,31,39,53,54,47,49,40,38,59,58,57,62,58,48,49,57,39
%N A282443 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 A282443 Peter Kagey, <a href="/A282443/b282443.txt">Table of n, a(n) for n = 1..10000</a>
%F A282443 a(n) = A282442(n) - 1.
%e A282443 For n = 4:
%e A282443 step size 1: 0 -> 1 -> 2 -> 3 -> 4;
%e A282443 step size 2: 4 -> 2 -> 0;
%e A282443 step size 3: 0 -> 3.
%e A282443 Because the walker cannot take four steps down, the biggest step size is 3.
%e A282443 Therefore a(4) = 3.
%Y A282443 Cf. A282442, A282444.
%K A282443 nonn
%O A282443 1,2
%A A282443 _Peter Kagey_, Feb 15 2017