On digital sequences associated with Pascal’s triangle

We consider the sequence of integers whose nth term has base-p expansion given by row Pascal’s triangle modulo p (where is a prime number). first present and generalize well-known relations concerning this sequence. Then, with great help Sloane’s On-Line Encyclopedia Integer Sequences, we show that it appears naturally as subsequence 2-regular Its study provides interesting surprisingly involves odious evil numbers, Nim-sum even Gray codes. Furthermore, examine similar sequences emerging from numbers involving alternating sum-of-digits p. This note ends discussion about pyramid built trinomial coefficients.