A383334 - OEIS

A383334

Square array read by antidiagonals: T(n,k) is the smallest positive weight of an n-tuple of nonnegative integers with a shortest vectorial addition chain of length k; n >= 1, k >= 0.

1, 2, 1, 3, 2, 1, 5, 3, 2, 1, 7, 4, 3, 2, 1, 11, 6, 4, 3, 2, 1, 19, 8, 5, 4, 3, 2, 1, 29, 12, 7, 5, 4, 3, 2, 1, 47, 20, 9, 6, 5, 4, 3, 2, 1, 71, 29, 13, 8, 6, 5, 4, 3, 2, 1, 127, 44, 20, 10, 7, 6, 5, 4, 3, 2, 1, 191, 70, 30, 14, 9, 7, 6, 5, 4, 3, 2, 1

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OFFSET

1,2

COMMENTS

See A383333 for details.

T(n,k) is the smallest positive degree of a monomial x_1^e_1*...*x_n^e_n that requires k multiplications, given x_1, ..., x_n.

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

Array begins:

n\k| 0 1 2 3 4 5 6 7 8

---+--------------------------

1 | 1 2 3 5 7 11 19 29 47

2 | 1 2 3 4 6 8 12 20 29

3 | 1 2 3 4 5 7 9 13 20

4 | 1 2 3 4 5 6 8 10 14

5 | 1 2 3 4 5 6 7 9 11

The smallest positive weight of a triple of nonnegative integers with a shortest addition chain of length 8 is T(3,8) = 20. Up to permutations, (3,4,13) is the only such triple, with a shortest addition chain [(1,0,0), (0,1,0), (0,0,1),] (0,0,2), (0,0,4), (0,1,4), (1,1,4), (2,2,8), (3,3,12), (3,3,13), (3,4,13).

CROSSREFS

Cf. A383333.

Rows: A003064 (n=1), A383332 (n=2).

Sequence in context: A173302 A251721 A251722 * A386214 A304100 A179314

Adjacent sequences: A383331 A383332 A383333 * A383335 A383336 A383337

KEYWORD

nonn,tabl

AUTHOR

Pontus von Brömssen, Apr 26 2025

STATUS

approved