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

Author

Pontus von Brömssen, Apr 27 2025

Keywords

• nonn

Comments

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.

Examples

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

Links

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

Crossrefs

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