By googling with the numbers 6.909 / 0.6909 / 13.81976 / 13.81758 /pi*e*phi
I didn’t get much hits and/or information.
Finally, I came to the site http://www.cosmicfingerprints.com/mathematics-of-dna/
And from there to the sites of Jean-Claude Perez, who has found a golden ratio in DNA-sequences.
The ratio of 0.690983, by Perez translated in 
is almost the same ratio as I did find.
Also a ratio found by Perez is the opposite: 
Look for his findings at:
"Codon populations in single-stranded whole human genome DNA Are fractal and fine-tuned by the Golden Ratio 1.618."
http://www.ncbi.nlm.nih.gov/pubmed/20658335
or
his book: Codex Biogenetics
https://sites.google.com/site/codexbiogenesis/home/resumes-des-chapitres
or http://golden-ratio-in-dna.blogspot.fr/
etc.
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Another interesting find on google was the philosophical and mathematical essay about Alfa , Pi*e*Phi (13.81758) from Dr. Zanglis.
Look at: http://www.flightboat.net/documents/Book%20Zagklis%20all%20Lock.pdf
(English text further in the document)
