Genetic recombination is a key mechanism of viral evolution in coronaviruses. In the case of SARS-CoV-2, the Spike protein (S) is a crucial genomic region where multiple recombination events have occurred. Previous research identified mathematical signatures associated with the recombinant feature in HIV-1. Based on evidence from experiments on SARS-CoV-2 unrelated to the present study, we hypothesized a relationship between a mathematical signature associated with the recombinant feature and arithmetic series with a ratio of 6 (nucleotide periodicity) in the S protein. We conducted a pilot study analyzing arithmetic series with a ratio of 6 in recombinant S proteins, finding a high presence of Thymine in series with an initial position multiple of 3. This pattern was not observed in other proteins like M and N. Repeating the process with non-recombinant sequences, we detected a similar pattern, although common nucleotides differed significantly between both sets. In this pilot study, we identified mathematical patterns associated with genetic recombination, specifically related to the third codon nucleotides. Our methodology was alignment-free and with minimal computational consumption. Our findings suggested the existence of mathematical signatures in the genome, especially in the encoded information of third codon nucleotides. Considering the diversity of perspectives and levels of information when reading and interpreting the genome may be necessary, acknowledging the existence of multiple layers of data and their interpretation.