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

1,1

Comments

There are only 14 radical narcissistic integers n < 10000.

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

Table of n, a(n) for n=1..14.

C. Rose, Pretty Wild Narcissistic Numbers - numbers that pwn (2006)

Wikipedia, Friedman number

Example

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

Mathematica

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

Crossrefs

Cf. A080035.

Sequence in context: A054259 A202455 A046319 * A043455 A267697 A232925

Adjacent sequences: A119707 A119708 A119709 * A119711 A119712 A119713

Keyword

base,nonn

Author

Colin Rose, Jun 10 2006

Status

approved