| viXra.org > Number Theory > viXra:2006.0056 |
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| viXra.org > Number Theory > viXra:2006.0056 |
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Number Theory |
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Authors: Claude H. R. Dequatre
A specific recursive algorithm and three fomulas have been used to generate integer sequences from prime and nonprime numbers seeds. After a few generations, some growing structures have been identified in these integer sequences, whereas such structures were absent when a subset of natural numbers was used as an alternative seed. The sum of the reciprocals of primes of these integer sequences, well fitted by models of the form a*ln(ln(n)) + b, were calculated. Their distances to that of the harmonic series summed only over the primes were estimated and compared to the Meissel-Mertens constant. Finally, the algorithm used with one of the three formulas led after a few iterations to the production of long primefree sequences containing large numbers and allowed to establish a so called primefree sequences conjecture.
Comments: 71 Pages. Comments are welcome
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