thing.el

(defun tmp:to-string (base to-power)
  (when (< 0 to-power)
    (concat
     (tmp:to-string base (1- to-power))
     (number-to-string
      (* base to-power)))))

(defun tmp:do-concat (base to-power)
  (string-to-number
   (tmp:to-string
    base to-power)))

(defun tmp:basep (n base &optional power)
  (let ((power (or power 1)))
    (let ((result (tmp:do-concat base power)))
      (cond
       ((= n result) base)
       ((< n result) 'too-big)
       (t (tmp:basep n base (1+ power)))))))

(defun tmp:p (n &optional base)
  (let ((base (or base 2))
        (result 'too-big))
    (while (eq result 'too-big)
      (setq result (tmp:basep n base))
      (setq base (1+ base)))
    (1- base)))