ON THE LAST DIGIT AND THE LAST NON-ZERO DIGIT OF nn IN BASE b
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In this paper we study the sequences defined by the last and the last non-zero digits of nn in base b. For the sequence given by the last digits of nn in base b, we prove its periodicity using different techniques than those used by W. Sierpinski and R. Hampel. In the case of the sequence given by the last non-zero digits of nn in base b (which had been studied only for b = 10) we show the non-periodicity of the sequence when b is an odd prime power and when it is even and square-free. We also show that if b = 22s the sequence is periodic and conjecture that this is the only such case.
Abstract
In this paper we study the sequences defined by the last and the last non-zero digits of nn in base b. For the sequence given by the last digits of nn in base b, we prove its periodicity using different techniques than those used by W. Sierpinski and R. Hampel. In the case of the sequence given by the last non-zero digits of nn in base b (which had been studied only for b = 10) we show the non-periodicity of the sequence when b is an odd prime power and when it is even and square-free. We also show that if b = 22s the sequence is periodic and conjecture that this is the only such case.
참고문헌 (14)
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