MacMahon's prime number of measurement | segmented number

The set of numbers generated by excluding the sums of two or more consecutive earlier members is called the prime numbers of measurement, or sometimes the segmented numbers. The first few terms are 1, 2, 4, 5, 8, 10, 14, 15, 16, 21, ... (OEIS A002048). Excluding two and three terms gives the sequence 1, 2, 4, 5, 8, 10, 12, 14, 15, 16, 19, 20, 21, ... (OEIS A005242).