A383143 -id:A383143 - cp's OEIS frontend

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

Jinyuan Wang, Apr 17 2025

			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).

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

Cf. A003064, A128998, A383001, A383143.

a(n) >= A003064(n).

A383337 Number of integers with a shortest addition-multiplication-exponentiation chain of length n.

Original entry on oeis.org

1, 1, 2, 7, 45, 485

Offset: 0

Pontus von Brömssen, Apr 27 2025

			Only 1 has an addition-multiplication-exponentiation chain of length 0, so a(0) = 1.
Only 2 has a shortest chain of length 1, so a(1) = 1.
3 and 4 have shortest chains of length 2, so a(2) = 2.
5, 6, 8, 9, 16, 27, and 256 have shortest chains of length 3, so a(3) = 7.

Cf. A003065, A383002, A383143, A383335, A383336.

cp's OEIS Frontend

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

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