A265692 -id:A265692 - cp's OEIS frontend

A265690 Cardinality of shortest addition chain for n.

1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 6, 5, 6, 6, 7, 6, 7, 7, 7, 6, 7, 7, 7, 7, 8, 7, 8, 6, 7, 7, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 9, 7, 8, 8, 8, 8, 9, 8, 9, 8, 9, 9, 9, 8, 9, 9, 9, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 9, 9, 9, 9, 10, 8, 9, 9, 9, 9, 9, 9, 10, 9, 10, 9, 10, 9, 10, 10, 10, 8, 9, 9, 9, 9

Offset: 1

Franklin T. Adams-Watters, Dec 13 2015

nonn

The cardinality of an addition chain is the number of terms in it, including the initial 1; hence it is one more than the length of the chain (A003313).

Wikipedia, Addition chain

Cf. A003313 (much more information and links), A265691, A265692.

a(n) = A003313(n) + 1.

A265691 Irregular triangle read by rows: row n gives lexicographically first addition chain of minimal length for n.

Original entry on oeis.org

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

Offset: 1

Franklin T. Adams-Watters, Dec 13 2015

The addition chains in this sequence for 1, 2, 3, 7 start respectively with 1, 1,2, 1,2,3, and 1,2,3,4. Are there minimal addition chains starting 1,2,3,4,5? 1,2,...,n for larger n?

Needs a b-file.

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

Cf. A265690 (row lengths), A265692 (largest).

cp's OEIS Frontend

A265690 Cardinality of shortest addition chain for n.

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