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A020656
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Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 6.
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28
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0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 38, 42, 43, 44, 45, 46, 48, 49, 50, 51, 58, 59, 61, 62, 63, 64, 65, 67, 68, 70, 72, 76, 84, 86, 87, 88, 89, 90, 92, 95, 96, 97, 98, 99, 102, 103, 106, 110, 113, 114, 116, 117, 119, 121
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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5 is excluded since (0,1,2,3,4,5) would be a 6-term AP.
10 is excluded since (0,2,4,6,8,10) would be a 6-term AP.
Idem for 15 and 20.
25 is not excluded, but after 25 (1,6,11,16,21,26) would be a 6-AP, and similarly all of 26 through 32 are excluded.
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PROG
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(PARI) A020656(n, show=1, i=0, o=6, u=0)={for(n=1, n, show&&print1(i, ", "); u+=1<<i; while(i++, for(s=1, i\(o-1), for(j=1, o-1, bittest(u, i-s*j)||next(2)); next(2)); next(2))); i} \\ M. F. Hasler, Jan 03 2016
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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
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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