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%I #32 Jan 09 2016 12:01:33
%S 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,
%T 36,38,42,43,44,45,46,48,49,50,51,58,59,61,62,63,64,65,67,68,70,72,76,
%U 84,86,87,88,89,90,92,95,96,97,98,99,102,103,106,110,113,114,116,117,119,121
%N Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 6.
%H David W. Wilson, <a href="/A020656/b020656.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A005838(n) - 1.
%e 5 is excluded since (0,1,2,3,4,5) would be a 6-term AP.
%e 10 is excluded since (0,2,4,6,8,10) would be a 6-term AP.
%e Idem for 15 and 20.
%e 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.
%o (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
%Y Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):
%Y 3-term AP: A005836 (>=0), A003278 (>0);
%Y 4-term AP: A005839 (>=0), A005837 (>0);
%Y 5-term AP: A020654 (>=0), A020655 (>0);
%Y 6-term AP: A020656 (>=0), A005838 (>0);
%Y 7-term AP: A020657 (>=0), A020658 (>0);
%Y 8-term AP: A020659 (>=0), A020660 (>0);
%Y 9-term AP: A020661 (>=0), A020662 (>0);
%Y 10-term AP: A020663 (>=0), A020664 (>0).
%K nonn
%O 1,3
%A _David W. Wilson_
%E Edited by _M. F. Hasler_, Jan 03 2016
%E Further edited (with new offset) by _N. J. A. Sloane_, Jan 04 2016
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