no. 4
Non recursive functions have transcendental generating series
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 23 (1989) no. 4, pp. 445-448 
@article{ITA_1989__23_4_445_0,
     author = {Cucker, Felipe and Gabarr\'o, Joaquim},
     title = {Non recursive functions have transcendental generating series},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {445--448},
     year = {1989},
     publisher = {EDP Sciences},
     volume = {23},
     number = {4},
     mrnumber = {1036695},
     zbl = {0683.03023},
     language = {en},
     url = {https://www.numdam.org/item/ITA_1989__23_4_445_0/}
}
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Cucker, Felipe; Gabarró, Joaquim. Non recursive functions have transcendental generating series. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 23 (1989) no. 4, pp. 445-448. https://www.numdam.org/item/ITA_1989__23_4_445_0/

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