; fibonacho numbers
 
(define (range . args)
  (case (length args)
    ((1) (range 0 (car args) (if (negative? (car args)) -1 1)))
    ((2) (range (car args) (cadr args) (if (< (car args) (cadr args)) 1 -1)))
    ((3) (let ((le? (if (negative? (caddr args)) >= <=)))
           (let loop ((x(car args)) (xs '()))
             (if (le? (cadr args) x)
                 (reverse xs)
                 (loop (+ x (caddr args)) (cons x xs))))))
    (else (error 'range "unrecognized arguments"))))
 
(define (iterate n f . bs)
  (let loop ((n n) (b (car bs)) (bs (cdr bs)) (xs '()))
    (if (zero? n) (reverse xs)
      (let ((new-bs (append bs (list (apply f b bs)))))
        (loop (- n 1) (car new-bs) (cdr new-bs) (cons b xs))))))
 
(define fibs (iterate 20 + 1 1))
 
(define (scan-left op base xs)
  (define (scan base xs)
    (if (null? xs) (list)
      (scan-left op (op base (car xs)) (cdr xs))))
  (cons base (scan base xs)))
 
(define sums (cdr (scan-left + 0 fibs)))
 
(define (restarts n)
  (define (max-less-or-equal n xs)
    (let loop ((prev 0) (xs xs))
      (if (< n (car xs)) prev
        (loop (car xs) (cdr xs)))))
  (let loop ((n n) (r 0))
    (if (zero? n) r
      (loop (- n (max-less-or-equal n sums)) (+ r 1)))))
 
; https://p...content-available-to-author-only...s.com/2016/12/20/highly-abundant-numbers
(define (records lt? xs) ; index and value at each new maximum
  (if (null? xs) (error 'records "no data")
    (let loop ((xs (cdr xs)) (k 1) (recs (list (cons 0 (car xs)))))
      (if (null? xs) (reverse recs)
        (if (lt? (cdar recs) (car xs))
            (loop (cdr xs) (+ k 1) (cons (cons k (car xs)) recs))
            (loop (cdr xs) (+ k 1) recs))))))
 
(define (fib n)
  (define (square x) (* x x))
  (cond ((zero? n) 0) ((or (= n 1) (= n 2)) 1)
        ((even? n) (let* ((n2 (quotient n 2)) (n2-1 (- n2 1)))
                     (* (fib n2) (+ (* 2 (fib n2-1)) (fib n2)))))
        (else (let* ((n2-1 (quotient n 2)) (n2 (+ n2-1 1)))
                (+ (square (fib n2-1)) (square (fib n2)))))))
 
(define (fibonacho n) (- (fib (+ n n 1)) n))
 
(display fibs) (newline)
(display sums) (newline)
(display (restarts 227)) (newline)
 
(for-each
  (lambda (idx/val)
    (display (cdr idx/val)) (display " ")
    (display (+ (car idx/val) 1)) (newline))
  (records < (map restarts (range 1 1000))))
 
(display (map fibonacho (range 1 50))) (newline)

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