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We propose a new alignment-free algorithm by constructing a compact vectorrepresentation on $\mathbb{R}^{24}$ of a DNA sequence of arbitrary length. Eachcomponent of this vector is obtained from a representative sequence, theelements of which are the values realized by a function $\Gamma$. This function$\Gamma$ acts on neighborhoods of arbitrary radius that are located atstrategic positions within the DNA sequence and carries complete informationabout the local distribution of frequencies of the nucleotides as a consequenceof the uniqueness of prime factorization of integer. The algorithm exhibitslinear time complexity and turns out to consume significantly small memory. Thetwo natural parameters characterizing the radius and location of theneighbourhoods are fixed by comparing the phylogenetic tree with the benchmarkfor full genome sequences of fish mtDNA datasets. Using these fittingparameters, the method is applied to analyze a number of genome sequences frombenchmark and other standard datasets. Our algorithm proves to becomputationally efficient compared to other well known algorithms when appliedon simulated dataset.

Similarity analysis of DNA sequences through local distribution of nucleotides in strategic neighborhood