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Challenges

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Challenges Length of a Sumac Sequence

BQN, 15 bytesSBCS {𝕨(1+βŠ’π•Š-)βŸœπ•©βŸ>0} Run online! A block function that takes $t_1$ as the left argument 𝕨 and $t_2$ as the right argument 𝕩. In BQN, π•Š indicates recursion on the current block ...

posted 3y ago by Marshall Lochbaum‭

Answer
#1: Initial revision by user avatar Marshall Lochbaum‭ · 2021-04-24T20:46:18Z (over 3 years ago)
# [BQN](https://mlochbaum.github.io/BQN/), 15 bytes<sup>[SBCS](https://github.com/mlochbaum/BQN/blob/master/commentary/sbcs.bqn)</sup>

```
{𝕨(1+βŠ’π•Š-)βŸœπ•©βŸ>0}
```

[Run online!](https://mlochbaum.github.io/BQN/try.html#code=U1Mg4oaQIHvwnZWoKDEr4oqi8J2Vii0p4p+c8J2VqeKNnz4wfQoKU1PCtMKo4p+oICMgRm9sZCAowrQpIHRvIGFwcGx5IHRvIGxpc3RzCiAg4p+oMTIwLDcx4p+pCiAg4p+oMTAxLDQy4p+pCiAg4p+oNTAwLDQ5OeKfqQogIOKfqDM4Nywx4p+pCiAg4p+oMywtMTI44p+pCiAg4p+oLTIsM+KfqQogIOKfqDMsMuKfqQrin6k=)

A block function that takes $t_1$ as the left argument `𝕨` and $t_2$ as the right argument `𝕩`. In BQN, `π•Š` indicates [recursion](https://mlochbaum.github.io/BQN/doc/block.html#self-reference) on the current block function. Inside the function the idea is just to return 0 if `𝕨≀0` and otherwise advance the sequence by one, recurse, and add one to the resulting sequence length.

```
{𝕨(1+βŠ’π•Š-)βŸœπ•©βŸ>0}
             0   # Default result of 0
 𝕨         ⍟>    # If 𝕨>0:
  (     )βŸœπ•©      # Use 𝕩 as right arg (left is still 𝕨)
     ⊒ -         # Right argument ⊒ and difference -
      π•Š          # Recurse
   1+            # Add one
```

The unrelated 0s for sequence length and minimum `𝕨` are combined by making 0 the right argument and using Repeat (`⍟`). With 0 repetitions, Repeat will return the right argument 0, and with 1 repetition, it will call the operand function, which immediately replaces 0 with `𝕩` using [After](https://mlochbaum.github.io/BQN/tutorial/combinator.html#before-and-after) (`𝕩` is a number, so it acts as a constant function).