论文标题
二进制序列
The Binary Two-Up Sequence
论文作者
论文摘要
二进制的两序序列是不同的非负整数的词素最早的序列，其属性是n-任期的二进制扩展与上一个楼层（N/2）术语的任何一个共同点。我们表明，该序列可以分解为``原子''，该序列是4、6或8个数字的序列，其二进制膨胀与某些模式相匹配，并且该序列是涉及原子的某种``单词''的限制形式。这导致了该术语的相当明确的公式，尤其是确定每个非零术语的猜想是2的最多两个权力的总和。
The Binary Two-Up Sequence is the lexicographically earliest sequence of distinct nonnegative integers with the property that the binary expansion of the n-th term has no 1-bits in common with any of the previous floor(n/2) terms. We show that the sequence can be decomposed into ``atoms'', which are sequences of 4, 6, or 8 numbers whose binary expansions match certain patterns, and that the sequence is the limiting form of a certain ``word'' involving the atoms. This leads to a fairly explicit formula for the terms, and in particular establishes the conjecture that every nonzero term is the sum of at most two powers of 2.
