Ordering of nested square roots of 2 according to the Gray code |
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| Authors: | Pierluigi Vellucci Alberto Maria Bersani |
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| Institution: | 1.Dipartimento di Scienze di Base e Applicate per l’Ingegneria,Sapienza University of Rome,Rome,Italy;2.Dipartimento di Ingegneria Meccanica e Aerospaziale,Sapienza University of Rome,Rome,Italy |
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| Abstract: | In this paper, we discuss some relations between zeros of Lucas–Lehmer polynomials and the Gray code. We study nested square roots of 2 applying a “binary code” that associates bits 0 and 1 to “plus” and “minus” signs in the nested form. This gives the possibility to obtain an ordering for the zeros of Lucas–Lehmer polynomials, which take the form of nested square roots of 2. |
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