A game with divisors and absolute differences of exponents |
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| Authors: | Cristian Cobeli Alexandru Zaharescu |
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| Institution: | 1. Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romaniacristian.cobeli@imar.ro;3. Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania;4. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA |
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| Abstract: | In this work, we discuss a number game that develops in a manner similar to that on which Gilbreath's conjecture on iterated absolute differences between consecutive primes is formulated. In our case the action occurs at the exponent level and there, the evolution is reminiscent of that in a final Ducci game. We present features of the whole field of the game created by the successive generations, prove an analogue of Gilbreath's conjecture and raise some open questions. |
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| Keywords: | Ducci game Gilbreath's conjecture primes game absolute differences Sierpinski triangle |
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