Van Eck sequence
The sequence is generated by following this pseudo-code:
Van Eck 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.
1: The first term is zero. Repeatedly apply: If the last term is *new* to the sequence so far then: 2: The next term is zero. Otherwise: 3: The next term is how far back this last term occured previousely.
- Example
Using 1:
0
Using 2:
0 0
Using 3:
0 0 1
Using 2:
0 0 1 0
Using 3: (zero last occured two steps back - before the one)
0 0 1 0 2
Using 1:
0 0 1 0 2 0
Using 3: (two last occured two steps back - before the zero)
0 0 1 0 2 0 2 2
Using 3: (two last occured one step back)
0 0 1 0 2 0 2 2 1
Using 3: (one last appeared six steps back)
0 0 1 0 2 0 2 2 1 6
...
- Task
- Create a function/proceedure/method/subroutine/... to generate the Van Eck sequence of numbers.
- Use it to display here, on this page:
- The first ten terms of the sequence.
- Terms 991 - to - 1000 of the sequence.
- Reference
Python
<lang python>def van_eck():
n, seen, val = 0, {}, 0 while True: yield val last = {val: n} val = n - seen.get(val, n) seen.update(last) n += 1
- %%
if __name__ == '__main__':
print("Van Eck: first 10 terms: ", list(islice(van_eck(), 10))) print("Van Eck: terms 991 - 1000:", list(islice(van_eck(), 1000))[-10:])</lang>
- Output:
Van Eck: first 10 terms: [0, 0, 1, 0, 2, 0, 2, 2, 1, 6] Van Eck: terms 991 - 1000: [4, 7, 30, 25, 67, 225, 488, 0, 10, 136]
Python: Alternate
The following stores the sequence so far in a list seen
rather than the first example that just stores last occurrences in a dict.
<lang python>def van_eck():
n = 0 seen = [0] val = 0 while True: yield val if val in seen[1:]: val = seen.index(val, 1) else: val = 0 seen.insert(0, val) n += 1</lang>
- Output:
As before.