A282444 -id:A282444 - cp's OEIS frontend

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.

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, 19, 27, 18, 23, 25, 20, 20, 30, 30, 19, 27, 24, 20, 31, 39, 32, 30, 38, 38, 24, 24, 34, 34, 50, 46, 31, 39, 53, 54, 47, 49, 40, 38, 59, 58, 57, 62, 58, 48, 49, 57, 39

Offset: 1

Peter Kagey, Feb 15 2017

nonn

			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, the biggest step size is 3.
Therefore a(4) = 3.

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

Cf. A282442, A282444.

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

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.

Original entry on oeis.org

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, 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, 1, 47, 49, 18, 21, 59, 3, 57, 1, 6, 17, 49, 57, 39, 43, 69, 9, 47, 51

Offset: 1

Peter Kagey, Feb 18 2017

nonn

If a(n) = 0 or a(n) = n, then A282443(n) = n and n is in A282444.

a(n) is bounded above by A282443(n) and bounded below by n - A282443(n).

			For n = 4:
step size 1: 0 -> 1 -> 2 -> 3 -> 4 (four steps);
step size 2: 4 -> 2 -> 0 (two steps);
step size 3: 0 -> 3 (one step).
Because the walker cannot take four steps down, a(4) = 3 (the final position).

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

Cf. A282442, A282443, A282444.

cp's OEIS Frontend

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.

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