# Fusc sequence

```ruby
func fusc(n) is cached {

    return 0 if n.is_zero
    return 1 if n.is_one

    n.is_even ? fusc(n/2) : (fusc((n-1)/2) + fusc(((n-1)/2)+1))
}

say ("First 61 terms of the Stern-Brocot sequence: ", 61.of(fusc).join(' '))

say "\nIndex and value for first term longer than any previous:"
printf("%15s : %s\n", "Index", "Value");

var (index=0, len=0)

5.times {
    index = (index..Inf -> first_by { fusc(_).len > len })
    len = fusc(index).len
    printf("%15s : %s\n", index.commify, fusc(index).commify)
}
```

## Output:

```
First 61 terms of the Stern-Brocot sequence: 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Index and value for first term longer than any previous:
          Index : Value
              0 : 0
             37 : 11
          1,173 : 108
         35,499 : 1,076
        699,051 : 10,946
```


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