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  • Decomposition into weight * level + jump and application to a new classification of primes

    Rémi Eismann - November 2012
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    Decomposition into weight * level + jump on the OeisWiki.
    arXiv:0711.0865 : Decomposition into weight * level + jump and application to a new classification of primes.
    The On-Line Encyclopedia of Integer Sequences (OEIS) - Neil J. A. Sloane.
    OEIS sequences submitted and/or edited.
    Graphs.
    New website, 200 sequences decomposed into weight * level + jump - 3D graphs (WebGL) - 2D graphs and 500 fisrt terms.
    3D Graphs (you must have a web browser compatible with webGL).

    The main goal of this site is to provide a new way to see certain numbers by their decomposition into weight * level + jump. This vision is both additive and multiplicative.
    Principle of decomposition : we choose the smallest weight such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference). The quotient will be the level.
    Principles of classification : if the number is not decomposable, it is not classified. if the weight is greater than the level then the number is classified by level, if not then it is classified by weight.
    This decomposition can be seen as a generalization of the sieve of Eratosthenes (which is the particular case of the sequence of natural numbers). Applied to prime numbers, this decomposition is used to obtain a new classification of primes.
    reismann (AT) free.fr (pubkey)

    Decomposition of prime numbers