We demonstrate some 10-periodic properties of the coefficients of two $q$-series related to partition numbers signed by the Legendre symbol $(\frac{a}{5})$ and to the Rogers-Ramanujan continued fraction $R(q)$.
Problems and results on determinants involving Legendre symbols
On determinants involving $(\frac{j+k}p)\pm(\frac{j-k}p)$
On a determinant involving linear combinations of Legendre symbols
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