A383337 -id:A383337 - 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.

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

Original entry on oeis.org

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

Offset: 0

Pontus von Brömssen, Apr 27 2025

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

			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).)

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

cp's OEIS Frontend

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

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