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A282574 The final position on a staircase of n steps during the following routine: 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 A282574 #11 Feb 19 2017 09:21:40
%S A282574 1,0,1,3,5,2,3,0,1,7,9,2,3,0,1,6,11,17,1,15,19,6,9,23,1,17,19,27,11,
%T A282574 23,25,12,13,4,5,19,27,14,19,31,39,10,13,6,7,22,23,14,15,0,5,31,39,53,
%U A282574 1,47,49,18,21,59,3,57,1,6,17,49,57,39,43,69,9,47,51
%N A282574 The final position on a staircase of n steps during the following routine: 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.
%C A282574 If a(n) = 0 or a(n) = n, then A282443(n) = n and n is in A282444.
%C A282574 a(n) is bounded above by A282443(n) and bounded below by n - A282443(n).
%H A282574 Peter Kagey, <a href="/A282574/b282574.txt">Table of n, a(n) for n = 1..10000</a>
%e A282574 For n = 4:
%e A282574 step size 1: 0 -> 1 -> 2 -> 3 -> 4 (four steps);
%e A282574 step size 2: 4 -> 2 -> 0 (two steps);
%e A282574 step size 3: 0 -> 3 (one step).
%e A282574 Because the walker cannot take four steps down, a(4) = 3 (the final position).
%Y A282574 Cf. A282442, A282443, A282444.
%K A282574 nonn
%O A282574 1,4
%A A282574 _Peter Kagey_, Feb 18 2017