A383332 Smallest positive weight of a pair of nonnegative integers with a shortest vectorial addition chain of length n.

1, 2, 3, 4, 6, 8, 12, 20, 29, 44, 70, 104

Offset: 0

Author

Pontus von Brömssen, Apr 26 2025

Keywords

• nonn
• hard
• more

Comments

See A383330 for details.

The weight of a pair is the sum of its elements.

Examples

			   n | a(n) | pairs (x,y) with x <= y, x+y = a(n), and shortest chain length n
  ---+------+-----------------------------------------------------------------
   0 |   1  | (0,1)
   1 |   2  | (0,2), (1,1)
   2 |   3  | (0,3), (1,2)
   3 |   4  | (1,3)
   4 |   6  | (1,5)
   5 |   8  | (1,7)
   6 |  12  | (1,11)
   7 |  20  | (1,19), (3,17)
   8 |  29  | (6,23)
   9 |  44  | (7,37)
  10 |  70  | (11,59)
  11 | 104  | (15,89)
		

Crossrefs

Row 2 of A383334.

Cf. A003064, A383330, A383331.