A119710 Radical narcissistic numbers: numbers n that can be expressed using just the digits of n (each digit used once only and in order from left to right) and the operators + - * / ^ and the radical symbol, but which are not already 'Good' Friedman numbers (i.e., the radical is needed for the solution to exist). Concatenation is allowed.

729, 1296, 1764, 2378, 2744, 2746, 3645, 4372, 4374, 4913, 5184, 6495, 6859, 8192

Offset: 1

Author

Colin Rose, Jun 10 2006

Keywords

• base
• nonn

Comments

There are only 14 radical narcissistic integers n < 10000.

Examples

			729 = (7 + 2)^sqrt(9);
2378 = -23 + sqrt(7^8).
		

References

• J. S. Madachy, Mathematics on Vacation, Thomas Nelson and Sons, (1966), pp. 163 - 175.
• Colin Rose, "Radical Narcissistic numbers", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 250-254.

Links

• C. Rose, Pretty Wild Narcissistic Numbers - numbers that pwn (2006)
• Wikipedia, Friedman number

Crossrefs

Cf. A080035.

Programs

Mathematica

Mathematica code to be available at: http://www.numq.com/pwn/