Geodesic
On algorithmical sequences belonging to the initial class of Grzegorczyk hierarchy
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 60-66

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It is proved that for any recursive sequence $f$ there exists a sequence $g$ of Grzegorczyk class $E^0$ such that $g(0),g(1),\dots$ is obtained from $f(0),f(1),\dots$ by replacing some members $f(i)$ by finite sequences $f(i),\dots,f(i)$. This implies that every recursively convergent recursive sequence of rational numbers can be represented by a functions from $E^0$. 
@article{ZNSL_1971_20_a6,
     author = {N. K. Kossovski},
     title = {On algorithmical sequences belonging to the initial class of {Grzegorczyk} hierarchy},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--66},
     publisher = {mathdoc},
     volume = {20},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a6/}
}
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N. K. Kossovski. On algorithmical sequences belonging to the initial class of Grzegorczyk hierarchy. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 60-66. http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a6/