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

1,3

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.

Links

Table of n, a(n) for n=1..95.

Wikipedia, Addition chain

Example

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
...

Crossrefs

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

Sequence in context: A265691 A334430 A214614 * A370263 A376308 A194976

Adjacent sequences: A265689 A265690 A265691 * A265693 A265694 A265695

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Dec 13 2015

Status

approved