MathDB
M 24

Source:

May 25, 2007
floor functioninductionRecursive Sequences

Problem Statement

Let kk be a given positive integer. The sequence xnx_n is defined as follows: x1=1x_1 =1 and xn+1x_{n+1} is the least positive integer which is not in {x1,x2,...,xn,x1+k,x2+2k,...,xn+nk}\{x_{1}, x_{2},..., x_{n}, x_{1}+k, x_{2}+2k,..., x_{n}+nk \}. Show that there exist real number aa such that xn=⌊an⌋x_n = \lfloor an\rfloor for all positive integer nn.
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