` 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 0, 3, ...`

This is the Van Eck’s Series.

Let’s go through it step by action.

Term 1: The very first term is 0.

Term 2: Given that we have not seen 0 previously, the 2nd term is 0.

Term 3: Given that we had actually seen a 0 prior to, one action back, the 3rd term is 1

Term 4: Given that we have not seen a 1 prior to, the 4th term is 0

Term 5: Given that we had actually seen a 0 prior to, 2 actions back, the 5th term is 2.

And so on&& mldr;

Your job is to discover the n_th number in Van Eck’s Series. (1-based)

## The Service in Python

### Alternative 1

```
from collections import Counter
c= Counter().
SEQ =[0]
for i in variety( 1000 ):.
n = SEQ[-1]
if not c[n]: c[n]= i.
SEQ.append( i-c[n]).
c[n]= i.
seq= SEQ. __ getitem __.
```

### Alternative 2

```
def dist( arr):.
for i in variety (1, len( arr)):.
if arr[-1-i] == arr[-1]:.
return i.
return 0.
def seq( n):.
s =[0, 0]
for _ in variety (n):.
s.append( dist( s)).
return s[n-1]
```

```
def seq( n):.
van, eck = [0], 0.
while n:= n - 1:.
van.insert( 0, eck:= van.index( eck, 1) if eck in van[1:] else 0).
return eck.
```

## Test cases to verify the service

```
from service import seq.
import test.
from random import randint.
@test. explain(" Sample tests:").
def tests():.
@test. it(" Little numbers").
def _():.
s =[0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6]
for i in variety (len( s)):.
test.assert _ equates to( seq( i +1), s[i]).
@test. it(' Larger numbers').
def __():.
s =[3, 1, 42, 0, 5, 15, 20, 0, 4, 32, 0, 3, 11,
18, 0, 4, 7, 0, 3, 7, 3, 2, 31, 0, 6, 31, 3,
6, 3, 2, 8, 33, 0, 9, 56, 0, 3, 8, 7, 19, 0,
5, 37, 0, 3, 8, 8, 1, 46, 0, 6, 23, 0]
for i in variety (len( s)):.
test.assert _ equates to( seq( i +50), s[i]).
@test. explain(' Random checks:'-RRB-.
def r():.
def dist( arr):.
for i in variety (1, len( arr)):.
if arr[-1-i] == arr[-1]:.
return i.
return 0.
def ref_sol( n):.
s =[0, 0]
for _ in variety (n):.
s.append( dist( s)).
return s[n-1]
@test. it(' 200 random tests:'-RRB-.
def _():.
for _ in variety (200 ):.
a = randint( 100, 1000).
exp = ref_sol( a).
test.assert _ equates to( seq( a), exp).
```