Given a computable sequence of natural numbers, it is a natural task to find a G\"odel number of a program that generates this sequence. It is easy to see that this problem is neither continuous nor computable. In algorithmic learning theory this problem is well studied from several perspectives and one question studied there is for which sequences this problem is at least learnable in the limit. Here we study the problem on all computable sequences and we classify the Weihrauch complexity of it. For this purpose we can, among other methods, utilize the amalgamation technique known from learning theory. As a benchmark for the classification we use closed and compact choice problems and their jumps on natural numbers, and we argue that these problems correspond to induction and boundedness principles, as they are known from the Kirby-Paris hierarchy in reverse mathematics. We provide a topological as well as a computability-theoretic classification, which reveal some significant differences.

翻译：给定一个自然数的可计算序列，寻找生成该序列的程序的哥德尔数是一项自然任务。容易看出，该问题既非连续也非可计算。在算法学习理论中，这一问题已从多个角度得到深入研究，其中一个研究问题是：对于哪些序列，该问题至少在极限意义上是可学习的。本文研究所有可计算序列上的该问题，并对其Weihrauch复杂度进行分类。为此，除其他方法外，我们可利用学习理论中已知的融合技术。作为分类基准，我们使用自然数上的闭与紧选择问题及其跳跃，并论证这些问题对应于逆向数学中Kirby-Paris层级所知的归纳与有界性原理。我们分别提供了拓扑与可计算性理论层面的分类，揭示了两者之间的一些显著差异。