CL-USER> (* (sqrt 10) (sqrt 10))
10.0
CL-USER> (* (coerce (sqrt 10) 'double-float) (coerce (sqrt 10) 'double-float))
10.000000242536998d0

(defun fig-square-p (n)
  "Check if the given N is a perfect square number.

 A000290 in the OEIS"
  (check-type n (integer 0 *))
  (= (floor (sqrt n)) (ceiling (sqrt n))))

(defun fig-square-p (n)
  "Check if the given N is a perfect square number.

 A000290 in the OEIS"
  (check-type n (integer 0 *))
  (= (floor (sqrt n)) (ceiling (sqrt n))))

(defun fibonaccip (n)
  "Check if the given number N is a Fibonacci number."
  (check-type n (integer 0 *))
  (or (fig-square-p (+ (* 5 (expt n 2)) 4))
      (fig-square-p (- (* 5 (expt n 2)) 4))))

(defun fibonacci (n)
  "Compute N's Fibonacci number."
  (check-type n (integer 0 *))
  (loop :for f1 = 0 :then f2
     :and f2 = 1 :then (+ f1 f2)
     :repeat n :finally (return f1)))

(defun seq-fibonaccies (n)
  "Return sequence of Fibonacci numbers upto N."
  (check-type n (integer 0 *))
  (loop :for i :from 1 :upto n
     :collect (fib i)))

PEHU> (loop :for i :from 0 :upto 7070 :when (fibonaccip i) :collect i)
(0 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 2889 3876 4181 5473
 6765 7070)
PEHU> (seq-fibonaccies 21)
(1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946)