科研之友
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摘要
For each of the functions f is an element of {phi, sigma, omega , tau} and every natural number K, we show that there are infinitely many solutions to the inequalities f(p(n) - 1) < f(p(n+1) - 1) < center dot center dot center dot < f(p(n+K) - 1), and similarly for f(p(n) - 1) > f(p(n+1) - 1) > center dot center dot center dot > f(p(n+ K) - 1). We also answer some questions of Sierpinski on the digit sums of consecutive primes. The arguments make essential use of Maynard and Tao's method for producing many primes in intervals of bounded length.
- 出版日期2015-8
