A383336 -id:A383336 - cp's OEIS frontend

A383335 Length of shortest addition-multiplication-exponentiation chain for n.

0, 1, 2, 2, 3, 3, 4, 3, 3, 4, 4, 4, 5, 5, 4, 3, 4, 4, 5, 4, 5, 5, 6, 4, 4, 5, 3, 4, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 5, 6, 6, 5, 5, 5, 6, 6, 6, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 4, 5, 5, 5, 5, 6, 5, 6, 5, 6, 6, 5, 6, 6, 6, 7, 5, 4, 5, 5, 5, 5, 6, 5

Offset: 1

Pontus von Brömssen, Apr 27 2025

nonn

An addition-multiplication-exponentiation chain for n is a finite sequence of numbers, starting with 1 and ending with n, in which each element except 1 equals x+y, x*y, or x^y for two preceding elements x and y (not necessarily distinct). The length of the chain is the number of elements in the chain, excluding 1.

			a(248) = 5 because the shortest addition-multiplication-exponentiation chain for 248 has length 5: (1, 2, 3, 5, 243, 248).

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Cf. A003313, A128998, A230697, A383336, A383337.

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

A383335 Length of shortest addition-multiplication-exponentiation chain for n.

Views

Author

Keywords

Comments

Examples

Links