OFFSET
1,1
COMMENTS
Consider the lexicographically earliest sequence of nonnegative numbers that does not contain the arithmetic mean of any pair of terms (such sequences are called 3-free sequences as they do not contain 3-term arithmetic progressions): 0,1,3,4 and so on. This sequence is Stanley sequence S(0,1). Remove numbers in the Stanley sequence from nonnegative integers and repeat the process of finding the earliest 3-free sequence. The result is this sequence.
When written in base three these are numbers that contain exactly one 2 that might be followed by zeros.
LINKS
Tanya Khovanova and Kevin Wu, Base 3/2 and Greedily Partitioned Sequences, arXiv:2007.09705 [math.NT], 2020.
EXAMPLE
Removing the Stanley sequence from nonnegative integers we get sequence A074940: 2, 5, 6, 7, 8, 11, 14, 15, 16, 17, 18 (Numbers having at least one 2 in their ternary representation). Our new sequence starts with 2,5,6. It can't contain 7 as 5,6,7 form an arithmetic progression. It can't contain 8 as 2,5,8 form an arithmetic progression. The next term is 11.
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and PRIMES STEP Junior, Jan 13 2019
STATUS
approved