A292836 a(n) is the minimum number of steps to a terminal state during the following procedure: start with n piles each containing one stone; any number of stones can be transferred between piles of equal size.

0, 1, 1, 3, 3, 4, 4, 6, 7, 7, 8, 10, 10, 11, 11, 13, 14, 14, 15, 17, 17, 18, 18, 20, 21, 22, 23, 24, 24, 25, 26, 28, 29, 29, 30, 31, 32, 33, 33, 35, 36, 37, 38, 39, 39, 40, 41, 43, 44, 44, 45, 46, 47, 48, 48, 50, 51, 52, 53, 54, 54, 55, 56, 58, 59, 59, 60, 62, 62

Offset

1,4

Comments

A terminal state is one in which all pile sizes are different, that is, there are no legal remaining ways to move stones.

A121924 is the analogous sequence for when only one stone can be moved at a time.

A011371 is the analogous sequence for when all stones must be moved at once.

Both A011371 and A121924 are upper bounds for this sequence.

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..100

Example

For n = 6, two examples of a a(6) = 4 step walks to a terminal state are:
[1 1 1 1 1 1] -> [2, 1, 1, 1, 1] -> [2, 2, 1, 1] -> [3, 1, 1, 1] -> [3, 2, 1], and
[1 1 1 1 1 1] -> [2, 1, 1, 1, 1] -> [2, 2, 1, 1] -> [2, 2, 2] -> [4, 2].

Crossrefs

Cf. A011371, A121924, A292726, A292729.

Sequence in context: A145814 A373797 A198465 * A240116 A007768 A180018

Adjacent sequences: A292833 A292834 A292835 * A292837 A292838 A292839

Keyword

nonn

Author

Peter Kagey, Sep 24 2017

Extensions

a(46) onwards from Bert Dobbelaere, Apr 07 2024

Status

approved