A086833 - OEIS

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

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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