  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.
