A086833 Minimum number of different addends occurring in any shortest addition chain of Brauer type for a given n.

1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 4, 5, 4, 4, 4, 3, 4, 4, 4, 4, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 4, 6, 5, 4, 6, 4, 5, 5, 5, 5, 5, 5, 4, 4, 5, 4, 5, 5, 5, 5, 5, 4, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 6, 4, 6, 7, 5, 6, 7, 5, 6, 6, 5, 5, 7, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5

Offset

1,4

Comments

a(12509) is first undefined element of this sequence because it is the smallest number that has no shortest addition chain of Brauer type. - Hugo Pfoertner, Jun 10 2006

Links

Table of n, a(n) for n=1..105.

Giovanni Resta, Tables of Shortest Addition Chains, computed by David W. Wilson.

Index to sequences related to the complexity of n

Example

a(23)=5 because 23=1+1+2+1+4+9+5 is the shortest addition chain for 23.
For n=9 there are A079301(9)=3 different shortest addition chains, all of Brauer type:
[1 2 3 6 9] -> 9=1+1+1+3+3 -> 2 different addends {1,3}
[1 2 4 5 9] -> 9=1+1+2+1+4 -> 3 different addends {1,2,4}
[1 2 4 8 9] -> 9=1+1+2+4+1 -> 3 different addends {1,2,4}
The minimum number of addends is 2, therefore a(9)=2.

Crossrefs

Cf. A003064, A003065, A003313, A005766, A008057, A008928, A008933, A079300, A079300, A079301.

Sequence in context: A125173 A054725 A064415 * A010764 A029383 A341737

Adjacent sequences: A086830 A086831 A086832 * A086834 A086835 A086836

Keyword

nonn

Author

Tatsuru Murai, Aug 08 2003

Extensions

Edited by Hugo Pfoertner, Jun 10 2006

Status

approved