Mysterious sequence in "Observationes cyklometricae" by Adam Adamandy Kochański
Antiquitates Mathematicae, Tome 4 (2010).
Problem of giving  the overall expression pattern within on the basis of his first few elements is well known to every mathematician. Puzzles of this type have something probably very appealing for anyone professionally involved in mathematics. If, however, we are dealing with during the initial elements that comes from a study published over three hundred years ago, the problem becomes even repeatedly more attractive.One such problem is the intriguing affair during which the first four elements, ie, 15,4697,5548,14774, gave Adam Adamandy Kochański in his work of 1685 concerning the rectification of the circle. This sequence helped him to create measurable approximations of the number π , but neither the formula for expression of general, or even methods of generating successive terms Kochański not reported. In this article, we will reconstruct the probable reasoning, which used the Kochański founding their approximate number of π , and also recreate the algorithm, which used to generate mentioned string.
Source: 
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     author = {Henryk Fuk\'s},
     title = {Mysterious sequence in {"Observationes} cyklometricae" by {Adam} {Adamandy} {Kocha\'nski}},
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Henryk Fukś. Mysterious sequence in "Observationes cyklometricae" by Adam Adamandy Kochański. Antiquitates Mathematicae, Tome 4 (2010). https://geodesic-test.mathdoc.fr/item/ANME_2010__4_293417/