Recaman's sequence

Recaman's sequence is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The Recamán's sequence generates Natural numbers.
Starting from zero, the n'th term a(n) is the previous term minus n i.e a(n) = a(n-1) - n but only if this is both positive and has not been previousely generated.

If the conditions don't hold then a(n) = a(n-1) + n.

Task

1. Generate and show here the first 15 members of the sequence.
2. Find and show here, the first duplicated number in the sequence.
3. Optionally: Find and show here, How many terms of the sequence are needed until all the integers 0..1000, inclusive, are generated.

Refeences

• A005132, The On-Line Encyclopedia of Integer Sequences.
• The Slightly Spooky Recamán Sequence, Numberphile video.

Python

<lang python>from itertools import islice

class Recamans():

   "Recamán's sequence generator callable class"
   def __init__(self):
       self.a = None   # Set of results so far
       self.n = None   # n'th term (counting from zero)
   
   def __call__(self):
       "Recamán's sequence  generator"
       nxt = 0
       a, n = {nxt}, 0
       self.a = a
       self.n = n
       yield nxt
       while True:
           an1, n = nxt, n + 1
           nxt = an1 - n
           if nxt < 0 or nxt in a:
               nxt = an1 + n
           a.add(nxt)
           self.n = n
           yield nxt

if __name__ == '__main__':

   recamans = Recamans()
   print("First fifteen members of Recamans sequence:", 
         list(islice(recamans(), 15)))

   so_far = set()
   for term in recamans():
       if term in so_far:
           print(f"First duplicate number in series is: a({recamans.n}) = {term}")
           break
       so_far.add(term)
   
   n = 1_000
   setn = set(range(n + 1))    # The target set of numbers to be covered
   for _ in recamans():
       if setn.issubset(recamans.a):
           print(f"Range 0 ..{n} is covered by terms up to a({recamans.n})")
           break</lang>

Output:

First fifteen members of Recamans sequence: [0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9]
First duplicate number in series is: a(24) = 42
Range 0 ..1000 is covered by terms up to a(328002)