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A376449
Smallest sum of addition chain for n.
1
0, 1, 3, 3, 6, 6, 10, 7, 12, 11, 17, 12, 19, 17, 21, 15, 24, 21, 29, 21, 31, 28, 34, 24, 36, 32, 39, 31, 46, 36, 48, 31, 48, 41, 52, 39, 56, 48, 58, 41, 62, 52, 64, 50, 66, 57, 74, 48, 73, 61, 75, 58, 82, 66, 83, 59, 86, 75, 90, 66, 93, 79, 94, 63, 96, 81, 101, 75, 103, 87, 112, 75, 112, 93, 111
OFFSET
1,3
COMMENTS
There are multiple ways to get a shortest addition chain (A003313), this sequence is the smallest sum of the possible chains.
LINKS
FORMULA
For n = 2^s, a(n)=s-1
EXAMPLE
Here are the smallest examples:
1 : 0 []
2 : 1 [1]
3 : 3 [1, 2]
4 : 3 [1, 2]
5 : 6 [1, 2, 3]
6 : 6 [1, 2, 3]
7 : 10 [1, 2, 3, 4]
8 : 7 [1, 2, 4]
9 : 12 [1, 2, 4, 5]
10 : 11 [1, 2, 3, 5]
11 : 17 [1, 2, 3, 5, 6]
12 : 12 [1, 2, 3, 6]
13 : 19 [1, 2, 3, 6, 7]
14 : 17 [1, 2, 3, 4, 7]
15 : 21 [1, 2, 3, 6, 9]
16 : 15 [1, 2, 4, 8]
17 : 24 [1, 2, 4, 8, 9]
18 : 21 [1, 2, 4, 5, 9]
19 : 29 [1, 2, 3, 4, 8, 11]
20 : 21 [1, 2, 3, 5, 10]
... etc
CROSSREFS
Sequence in context: A290966 A049318 A325861 * A079551 A182843 A358558
KEYWORD
nonn
AUTHOR
Roy van Rijn, Sep 23 2024
STATUS
approved