Still small enough to solve in a few lines:
http://www.complang.tuwien.ac.at/forth/programs/euler/63.fs
\ Problem:
\ The 5-digit number, 16807=75, is also a fifth power. Similarly, the
\ 9-digit number, 134217728=89, is a ninth power.
\ How many n-digit positive integers exist which are also an nth power?
\ They don't count 0^1 (0 is not deemed to be positive)
\ Solution:
\ 10^n produces a n+1-digit integer, so we need only look at bases 0-9.
: n-digits { n -- n2 }
\ number of n-th powers with n digits
\ for n=1, it does not count 0 and 1 (I correct for the 1 below)
\ this works by just seeing what the lowest x is that fits in
\ 10^(n-1), and then rounding x up to an integer
n 1- 0 d>f n 0 d>f f/ falog f>d drop 9 swap - ;
: solve ( -- )
1 1 begin ( n sum )
over n-digits dup 0> while
+ swap 1+ swap repeat
drop nip ;
solve . cr
- anton
--
M. Anton Ertl http://www.complang.tuwien.ac.at/anton/home.html
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