A230697 Length of shortest addition-multiplication 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, 4, 5, 5, 5, 6, 4, 5, 5, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 5, 6, 6, 5, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 7, 5, 6, 6, 6, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 5, 6, 6, 6, 7, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 7, 7, 5, 6, 6, 5, 5, 6, 6, 6, 6, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 7, 6, 6, 7, 7, 6, 5, 6, 6, 6, 5, 6, 6, 5, 6, 6

Offset

1,3

Links

Table of n, a(n) for n=1..130.

H. M. Bahig, On a generalization of addition chains: Addition-multiplication chains, Discrete Mathematics 308 (2008), 611-616

Gleb Ivanov, Python program.

Example

A shortest addition-multiplication chain for 16 is (1,2,4,16), of length 3.

Crossrefs

Cf. A003313, A128998, A173419, A005245, A354914.

Sequence in context: A322006 A173419 A099053 * A322163 A075167 A253555

Adjacent sequences: A230694 A230695 A230696 * A230698 A230699 A230700

Keyword

nonn

Author

Harry Altman, Oct 27 2013

Status

approved