A383336 Smallest number with shortest addition-multiplication-exponentiation chain of length n.

1, 2, 3, 5, 7, 13, 23, 79, 214, 1418, 5991

Offset: 0

Author

Pontus von Brömssen, Apr 27 2025

Keywords

• nonn
• hard
• more

Comments

For n >= 1, the largest number with shortest addition-multiplication-exponentiation chain of length n is A173566(n).

Examples

			a(7) = 79 because all smaller numbers have addition-multiplication-exponentiation chains of length at most 6, but the shortest chain for 79 has length 7. One such chain is (1, 2, 3, 5, 32, 37, 42, 79). (There are also such chains that do not use exponentiation, such as (1, 2, 3, 4, 5, 15, 75, 79).)
		

Crossrefs

Cf. A003064, A173566, A383001, A383142, A383335, A383337.