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).
Prime Number of Measurement
See also
Sum-Free SetExplore with Wolfram|Alpha
References
Guy, R. K. "MacMahon's Prime Numbers of Measurement." §E30 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 230-231, 1994.Sloane, N. J. A. Sequences A002048/M0972 and A005242/M0971 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Prime Number of MeasurementCite this as:
Weisstein, Eric W. "Prime Number of Measurement." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrimeNumberofMeasurement.html