signposts.el

(intern ":fact")
(intern ":expt")

(defun sp/fact (n)                      ; n!
  (if (> n 1)
      (* n (sp/fact (- n 1)))
    1))

(defun sp/term(op &rest rest)
  (cond ((eq op :fact) (cons 'sp/fact rest)) ; a!
        ((eq op :expt) (cons 'expt rest))    ; a^b
        t (error "bad op")))

(defun sp/poly (&rest terms) 
  terms)

(defun sp/eval-term (term)
  (eval term))

(defun sp/eval-poly (poly)
  (apply '+ (mapcar 'sp/eval-term poly)))

(defun sp/show-poly (poly)
  poly)

; (sp/eval-poly (sp/poly (sp/term :fact 5) (sp/term :expt 3 4) (sp/term :expt 2 5)))
;-> 233

; (sp/show-poly (sp/poly (sp/term :fact 5) (sp/term :expt 3 4) (sp/term :expt 2 5)))
; -> ((sp/fact 5) (expt 3 4) (expt 2 5))


; nearest power of k nearest n
(defun sp/nearest-power-of-k(n k)
  (let* ((lg (log n k))
         ;; two possible nearest values
         (a (expt k (floor lg)))
         (b (expt k (ceiling lg))))
    ;;  pick the closest one
    (if (< (- n a) (- b n))
        a
      b)))

;; ;; expected

;; 5, 3 -> 3
;; 32, 7 -> 49
;; 6, 3 -> 9

;; (sp/nearest-power-of-k 5 3)
;; 3

;; (sp/nearest-power-of-k 6 3)
;; 9

;; (sp/nearest-power-of-k 32 7)
;; 49

(defun sp/primes-below(n)
  )

(defun sp/nearest-prime-power-below-n(n)
)