A383142 Smallest positive integer with shortest addition-subtraction chain of length n.

1, 2, 3, 5, 7, 11, 19, 29, 53, 87, 151, 267, 461, 811, 1383, 2357, 4277, 7499, 14003, 25931, 44269, 87773, 152947, 271563

Offset: 0

Author

Jinyuan Wang, Apr 17 2025

Keywords

• nonn
• hard
• more

Examples

			a(8) = 53 because 53 is the smallest positive integer k such that A128998(k) = 8. An example of a shortest addition-subtraction chain for 53 is (1 2 3 4 7 14 25 28 53). a(8) > A003064(8) because an optimal chain for A003064(8) = 47 has length 7: (1 2 3 6 12 24 23 47).
		

Links

• Neill Clift, Addition Subtraction Chains.
• Index to sequences related to the complexity of n

Crossrefs

Cf. A003064, A128998, A383001, A383143.

Formula

a(n) >= A003064(n).