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

1,3

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.

Links

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

Example

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

Crossrefs

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

Sequence in context: A322006 A173419 A099053 * A384384 A230697 A322163

Adjacent sequences: A383332 A383333 A383334 * A383336 A383337 A383338

Keyword

nonn

Author

Pontus von Brömssen, Apr 27 2025

Status

approved