%I #8 Jan 23 2019 02:57:27

%S 7,8,16,17,19,20,34,35,43,44,46,47,55,56,88,89,97,98,100,101,115,116,

%T 124,125,127,128,136,137,163,164,250,251,259,260,262,263,277,278,286,

%U 287,289,290,298,299,331,332,340,341,343,344,358,359,367,368,370,371,379,380,406,407,487,488,736,737,745,746,748,749

%N The third greedy 3-free sequence on nonnegative integers.

%C Consider the lexicographically earliest sequence of nonnegative integers 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 next earliest 3-free sequence, which is sequence A323398. We get this sequence on the next iteration.

%C When represented in ternary this sequence consists of integers ending in 1 or 2, and there is exactly one digit 2 before that that might be followed by zeros.

%Y Cf. A005836, A074940, A323398, A323419.

%K nonn

%O 1,1

%A _Tanya Khovanova_ and PRIMES STEP Junior, Jan 14 2019