mersenneforum.org Generalized Mersenne Sequence continuation
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 2017-03-23, 23:27 #1 carpetpool     "Sam" Nov 2016 1010010002 Posts Generalized Mersenne Sequence continuation Given the Mersenne Sequence 2^n-1, it can be modeled using the true equation: 2 - 1 = 1 One generalization includes fixing 2 to a and forming the equation and sequence: a - 1 = b (a^n-1)/b Another generalization include: a - b = c (a^n-b^n)/c What is the proper Generalized Mersenne Sequence(s) for the "base" equation: x*a - y*b = z*c in terms of (a, b, c, x, y, z) and the exponent n? In the case of (a^n-b^n)/c, (x, y, z) = 1. What about when one, both, or all of (x, y, z) > 1? What is the closed form similar to (a^n-b^n)/c with the same sequence properties?
2017-03-23, 23:42   #2
science_man_88

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Jul 2009
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Quote:
 Originally Posted by carpetpool Given the Mersenne Sequence 2^n-1, it can be modeled using the true equation: 2 - 1 = 1 One generalization includes fixing 2 to a and forming the equation and sequence: a - 1 = b (a^n-1)/b Another generalization include: a - b = c (a^n-b^n)/c What is the proper Generalized Mersenne Sequence(s) for the "base" equation: x*a - y*b = z*c in terms of (a, b, c, x, y, z) and the exponent n? In the case of (a^n-b^n)/c, (x, y, z) = 1. What about when one, both, or all of (x, y, z) > 1? What is the closed form similar to (a^n-b^n)/c with the same sequence properties?
https://en.wikipedia.org/wiki/Mersen...eneralizations shows complex number generalizations as well.

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