The Klarner-Rado sequence lists in increasing order the smallest set of positive integers containing 1 and closed under the maps 
, 
, and 
. Its first terms are 1, 2, 4, 5, 8, 9, 10, 14, 15,
16, 17, ... (OEIS A005658).
Klarner-Rado Sequence
See also
Double-Free SetExplore with Wolfram|Alpha
References
Guy, R. K. "Klarner-Rado Sequences." §E36 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 237, 1994.Klarner, D. A. and Rado, R. "Linear Combinations of Sets of Consecutive Integers." Amer. Math. Monthly 80, 985-989, 1973. https://doi.org/10.1080/00029890.1973.11993430.Sloane, N. J. A. Sequence A005658/M0969 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Klarner-Rado SequenceCite this as:
Weisstein, Eric W. "Klarner-Rado Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Klarner-RadoSequence.html