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.

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

1,4

Comments

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).

Links

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

Example

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).

Crossrefs

Cf. A282442, A282443, A282444.

Sequence in context: A115406 A059246 A091276 * A076562 A306220 A057673

Adjacent sequences: A282571 A282572 A282573 * A282575 A282576 A282577

Keyword

nonn

Author

Peter Kagey, Feb 18 2017

Status

approved