A122352 Knuth's power tree represented by parent node number.

0, 1, 2, 2, 3, 3, 5, 4, 6, 5, 10, 6, 10, 7, 10, 8, 16, 9, 14, 10, 14, 11, 13, 12, 15, 13, 18, 14, 28, 15, 28, 16, 17, 17, 21, 18, 36, 19, 26, 20, 40, 21, 40, 22, 30, 23, 42, 24, 48, 25, 48, 26, 52, 27, 44, 28, 38, 29, 31, 30, 56, 31, 42, 32, 64, 33, 66, 34, 46, 35, 57, 36, 37, 37

Offset

1,3

Comments

This method of representing the power tree is suggested by exercise 10 in Section 4.6.3 page 481 TAOCP Vol. 2.

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.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Hugo Pfoertner, Addition chains

Example

The power tree sequence for 54 is 1,2,3,6,9,18,27,54, so a(54) = 27.

Crossrefs

Cf. A114622.

Sequence in context: A300271 A252461 A323608 * A338903 A362830 A248519

Adjacent sequences: A122349 A122350 A122351 * A122353 A122354 A122355

Keyword

nonn

Author

Franklin T. Adams-Watters, Aug 30 2006

Status

approved