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A323419
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The fourth greedy 3-free sequence on nonnegative integers.
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2
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21, 22, 24, 25, 48, 49, 51, 52, 57, 58, 60, 61, 102, 103, 105, 106, 129, 130, 132, 133, 138, 139, 141, 142, 165, 166, 168, 169, 264, 265, 267, 268, 291, 292, 294, 295, 300, 301, 303, 304, 345, 346, 348, 349, 372, 373, 375, 376, 381, 382, 384, 385, 408, 409, 411, 412, 489, 490, 492, 493, 750, 751, 753, 754, 777, 778, 780
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OFFSET
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1,1
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COMMENTS
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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. The next iteration produces sequence A323418. The fourth iteration produces this sequence.
When represented in ternary this sequence consists of integers ending in 10, 11, 20 or 21, and there is exactly one digit 2 before that that might be followed by zeros.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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