

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.


1



729, 1296, 1764, 2378, 2744, 2746, 3645, 4372, 4374, 4913, 5184, 6495, 6859, 8192
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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, (20042005), pp. 250254.


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



