MathDB
Odd Integer Sequence

Source:

December 31, 2005
floor function

Problem Statement

In the non-decreasing sequence of odd integers {a1,a2,a3,…}={1,3,3,3,5,5,5,5,5,…}\{a_1,a_2,a_3,\ldots \}=\{1,3,3,3,5,5,5,5,5,\ldots \} each odd positive integer kk appears kk times. It is a fact that there are integers bb, cc, and dd such that for all positive integers nn, an=b⌊n+c⌋+d, a_n=b\lfloor \sqrt{n+c} \rfloor +d, where ⌊x⌋\lfloor x \rfloor denotes the largest integer not exceeding xx. The sum b+c+db+c+d equals (A) 0(B) 1(C) 2(D) 3(E) 4\text{(A)} \ 0 \qquad \text{(B)} \ 1 \qquad \text{(C)} \ 2 \qquad \text{(D)} \ 3 \qquad \text{(E)} \ 4
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