A265692 Irregular triangle read by rows: lexicographically last addition chain of minimal length for n.

1, 1, 2, 1, 2, 3, 1, 2, 4, 1, 2, 4, 5, 1, 2, 4, 6, 1, 2, 4, 6, 7, 1, 2, 4, 8, 1, 2, 4, 8, 9, 1, 2, 4, 8, 10, 1, 2, 4, 8, 10, 11, 1, 2, 4, 8, 12, 1, 2, 4, 8, 12, 13, 1, 2, 4, 8, 12, 14, 1, 2, 4, 5, 10, 15, 1, 2, 4, 8, 16, 1, 2, 4, 8, 16, 17, 1, 2, 4, 8, 16, 18, 1, 2, 4, 8, 16, 18, 19, 1, 2, 4, 8, 16, 20

Offset: 1

Author

Franklin T. Adams-Watters, Dec 13 2015

Keywords

• nonn
• tabf

Comments

While addition chains are normally entered with terms in increasing order, the usual definition requires only that each term follows a pair of terms of which it is the sum. This sequence will eventually contain rows that are not monotonic; in particular, any non-Brauer number will have such a chain. What is the first number whose chain in this sequence is not monotonic?

47 is the first number with a non-monotonic lexicographically last addition chain of minimal length: [1, 2, 4, 8, 16, 5, 21, 42, 47]. - Alois P. Heinz, Dec 22 2015

Needs a b-file.

Examples

			The table starts:
1
1 2
1 2 3
1 2 4
1 2 4 5
1 2 4 6
1 2 4 6 7
1 2 4 8
...
		

Links

• Wikipedia, Addition chain

Crossrefs

Cf. A265690 (row lengths), A265691 (smallest).