论文标题
关于与Pascal的三角形相关的数字序列
On digital sequences associated with Pascal's triangle
论文作者
论文摘要
我们考虑了$ n $ th $ n $ p $扩展的整数序列，由$ n $ n $ th ROW PASCAL的三角形模型$ p $ P $（其中$ p $是质量数字）。我们首先提出并概括有关此序列的众所周知的关系。然后，在Sloane在线序列的在线百科全书的大力帮助下，我们表明它自然是$ 2 $ regratular序列的子序列。它的研究提供了有趣的关系，令人惊讶的是涉及可恶和邪恶的数字，nim-sum甚至灰色代码。此外，我们研究了从涉及交替数字款模型〜$ p $的质数中出现的类似序列。本说明以有关涉及三项元素系数的Pascal金字塔的讨论结尾。
We consider the sequence of integers whose $n$th term has base-$p$ expansion given by the $n$th row of Pascal's triangle modulo $p$ (where $p$ is a prime number). We first present and generalize well-known relations concerning this sequence. Then, with the great help of Sloane's On-Line Encyclopedia of Integer Sequences, we show that it appears naturally as a subsequence of a $2$-regular sequence. Its study provides interesting relations and surprisingly involves odious and evil numbers, Nim-sum and even Gray codes. Furthermore, we examine similar sequences emerging from prime numbers involving alternating sum-of-digits modulo~$p$. This note ends with a discussion about Pascal's pyramid involving trinomial coefficients.
