On digital sequences associated with Pascal's triangle (Q2696006)

In the related paper, the authors study the sequence of integers whose \(n\)th term has a base-\(p\) expansion given by the \(n\)th row of Pascal's triangle modulo \(p\) (where \(p\) is a prime number). They first present and generalize well-known relations concerning this sequence. Then, with the great help of Sloane's On-Line Encyclopedia of Integer Sequences, the authors 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. Moreover, the authors examine similar sequences emerging from prime numbers involving alternating sum-of-digits modulo \(p\). Finally, they provide a discussion about Pascal's pyramid built with trinomial coefficients.