euler_29.scm

#!/usr/bin/csi -bq

#|
Distinct powers
Problem 29

Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

    2^2=4, 2^3=8, 2^4=16, 2^5=32
    3^2=9, 3^3=27, 3^4=81, 3^5=243
    4^2=16, 4^3=64, 4^4=256, 4^5=1024
    5^2=25, 5^3=125, 5^4=625, 5^5=3125

If they are then placed in numerical order, with any repeats removed, we get 
the following sequence of 15 distinct terms:

    4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 
and 2 ≤ b ≤ 100?
|#

(define (expo a b lim)
  (cond
    ((eq? a 1) 
     '())
    ((eq? b 2) 
     (cons (expt a b) 
           (expo (sub1 a) lim lim)))
    (else 
     (cons (expt a b) 
           (expo a (sub1 b) lim)))))

(define (counter l)
  (cond
    ((null? l) 
     0)
    ((member (car l) (cdr l)) 
     (counter (cdr l)))
    (else 
     (add1 (counter (cdr l))))))

(define n 100)
(define l (expo n n n))
(display (counter l))