#lang racket

(define (accumulate op initial sequence)
  (if (null? sequence)
      initial
      (op (car sequence)
          (accumulate op initial (cdr sequence)))))

(define (horner-eval x coefficient-sequence)
  (accumulate (lambda (this-coeff higher-terms)
                (+ this-coeff (* x higher-terms)))
              0
              coefficient-sequence))


(define (accumulate-n op init seqs)
  (if (null? (car seqs))
      null
      (cons (accumulate op init (map car seqs))
            (accumulate-n op init (map cdr seqs)))))

(define (count-leaves t)
  (accumulate + 0 (map (lambda (x)
                         (if (not (pair? x))
                             1
                             (count-leaves x))) t)))

(define (flatmap proc seq)
  (accumulate append null (map proc seq)))

(define (prime? x) (= (modulo x 2) 1))

(define (prime-sum? pair)
  (prime? (+ (car pair) (cadr pair))))

(define (make-pair-sum pair)
  (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))

(define (enumerate-interval low high)
  (if (> low high)
      null
      (cons low (enumerate-interval (+ 1 low) high))))

(define (unique-pairs n)
  (flatmap (lambda (i)
             (map (lambda (j) (list j i))
                  (enumerate-interval 1 (- i 1))))
           (enumerate-interval 1 n)))

(define (prime-sum-pairs n)
  (map make-pair-sum
       (filter prime-sum? (unique-pairs n))))

(define (is-eq-s? s triplet)
  (= s (accumulate + 0 triplet)))

(define