The distribution of codons in the nearly universal genetic code is a long discussed issue. At the atomic level, the numeral series 2x(2) (x=5-0) lies behind electron shells and orbitals. Numeral series appear in formulas for spectral lines of hydrogen. The question here was if some similar scheme could be found in the genetic code. A table of 24 codons was constructed (synonyms counted as one) for 20 amino acids, four of which have two different codons. An atomic mass analysis was performed, built on common isotopes. It was found that a numeral series 5 to 0 with exponent 2/3 times 10(2) revealed detailed congruency with codon-grouped amino acid side-chains, simultaneously with the division on atom kinds, further with main 3rd base groups, backbone chains and with codon-grouped amino acids in relation to their origin from glycolysis or the citrate cycle. Hence, it is proposed that this series in a dynamic way may have guided the selection of amino acids into codon domains. Series with simpler exponents also showed noteworthy correlations with the atomic mass distribution on main codon domains; especially the 2x(2)-series times a factor 16 appeared as a conceivable underlying level, both for the atomic mass and charge distribution. Furthermore, it was found that atomic mass transformations between numeral systems, possibly interpretable as dimension degree steps, connected the atomic mass of codon bases with codon-grouped amino acids and with the exponent 2/3-series in several astonishing ways. Thus, it is suggested that they may be part of a deeper reference system.

The genetic code was studied hypothesizing that it has a mathematical underground like numerical schemes on the atomic level. A preceding article, including general arguments about this approach (

The search for regularities in the background for the genetic code and its codon assignments is here further developed, earlier shown to have many correlations with numeral series of integers 5 →0 with different exponents. The atomic mass analysis here counts on 20 + 4 double-coded amino acids, here including Ile AUA as such. A central finding here is that the C-skeleton seems to build on an hierarchical development of the mentioned basic series giving top numbers equal to those returning in side-chain divisions and on first three levels those of C-atoms in base-pair domains. It can very elementary explain the 3/2-division in the weight series. A few main results from earlier articles are shortly recapitulated, since it’s shown here that an x­3-series times 15 (x = integers 5 → 0) joins those earlier aspects and add new ones. It’s found also that atoms with valences 4 + 3 relative those with 2 + 1 make up a 3 to 1-division in both base-pair groups of codon domains, strengthening the earlier observation of valences as one important guiding principle in the relation between codons and domains of amino acids; valences of the atoms which in themselves make up a basic series 5 → 0 in the code when phosphorus P is included. Finally, fundamental factors in the code are gathered, where step 4 →3 seems reign at bottom of the code and number 7, exactly mean value of all atoms.