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
Offset: 1
Examples
A shortest addition-multiplication chain for 16 is (1,2,4,16), of length a(16) = 3. A shortest addition-multiplication chain for 281 is (1,2,4,5,16,25,256,281), of length a(281) = 7. This is the first case where not all terms in some shortest chain are the sum or product of the immediately preceding term and one more preceding term. In other words, 281 is the smallest of the analog of non-Brauer numbers (A349044) for addition-multiplication chains. The next ones are 913, 941, 996, 997, 998, 1012, 1077, 1079, 1542, 1572, 1575, 1589, 1706, 1792, 1795, 1816, 1864, ... . - _Pontus von Brömssen_, May 02 2025
Links
- Jinyuan Wang, Table of n, a(n) for n = 1..10000
- H. M. Bahig, On a generalization of addition chains: Addition-multiplication chains, Discrete Mathematics 308 (2008), 611-616.
- Gleb Ivanov, Python program.
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