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

Author

Franklin T. Adams-Watters, Dec 13 2015

Keywords

• nonn

Comments

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).

Links

• Wikipedia, Addition chain

Crossrefs

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

Formula

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