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

Author

Franklin T. Adams-Watters, Aug 30 2006

Keywords

• nonn

Comments

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

Examples

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

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

Crossrefs

Cf. A114622.