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A020657
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Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 7.
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43
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0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 84, 85
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OFFSET
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1,3
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COMMENTS
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Also the set of numbers with no "6" in their base-7 representation; see Gerver-Ramsey, also comments in A020654. - Nathaniel Johnston, Jun 27 2011
Up to the offset, identical to A037470. There are lexicographically earlier, but non-monotonic sequences which do not contain a 7-term AP, e.g., starting with 0,0,0,0,0,0,1,0,... - M. F. Hasler, Oct 05 2014
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LINKS
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MAPLE
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seq(`if`(numboccur(6, convert(n, base, 7))=0, n, NULL), n=0..85); # Nathaniel Johnston, Jun 27 2011
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MATHEMATICA
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PROG
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(PARI) a(n)=vector(#n=digits(n-1, 6), i, 7^(#n-i))*n~ \\ M. F. Hasler, Oct 05 2014
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CROSSREFS
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Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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