In this note, we show that if b > 1 is an integer, f(X) ∈ Q[X] is an integer valued quadratic polynomial and K > 0 is any constant, then the b-adic number ∑n≥0 (an / bf(n)), where an ∈ Z and 1 ≤ |an| ≤ K for all n ≥ 0, is neither rational nor quadratic.
@article{urn:eudml:doc:44537,
title = {.121221222... is not quadratic.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {18},
year = {2005},
pages = {353-362},
zbl = {1083.11045},
mrnumber = {MR2166514},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44537}
}
Luca, Florian. .121221222... is not quadratic.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 353-362. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44537/