OFFSET

1,1

COMMENTS

The first three terms are given in Knuth's TAOCP, Vol. 2. The sequence is based on a table of shortest addition chain lengths computed by Neill M. Clift, see link to Achim Flammenkamp's web page given at A003313.

REFERENCES

D. E. Knuth, The Art of Computer Programming Third Edition. Vol. 2, Seminumerical Algorithms. Chapter 4.6.3 Evaluation of Powers, Page 464. Addison-Wesley, Reading, MA, 1997.

EXAMPLE

a(1)=77 because the power tree construction produces the chain 1 2 3 5 7 14 19 38 76 77 requiring 9 additions, whereas there are 4 shortest chains that come along with 8 additions, e.g. 1 2 4 8 9 17 34 43 77.

CROSSREFS

Cf. A114622 [The power tree (as defined by Knuth)], A003313 [Length of shortest addition chain for n], A115614 [numbers such that Knuth's power tree method produces a result deficient by 2], A115615 [numbers such that Knuth's power tree method produces a result deficient by 3], A115616 [smallest number for which Knuth's power tree method produces an addition chain n terms longer than the shortest possible chain].

KEYWORD

nonn

AUTHOR

Hugo Pfoertner and Neill M. Clift, Jan 31 2006

STATUS

approved