

A020656


Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 6.


28



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

1,3


LINKS

David W. Wilson, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A005838(n)  1.


EXAMPLE

5 is excluded since (0,1,2,3,4,5) would be a 6term AP.
10 is excluded since (0,2,4,6,8,10) would be a 6term AP.
Idem for 15 and 20.
25 is not excluded, but after 25 (1,6,11,16,21,26) would be a 6AP, and similarly all of 26 through 32 are excluded.


PROG

(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\(o1), for(j=1, o1, bittest(u, is*j)next(2)); next(2)); next(2))); i} \\ M. F. Hasler, Jan 03 2016


CROSSREFS

Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):
3term AP: A005836 (>=0), A003278 (>0);
4term AP: A005839 (>=0), A005837 (>0);
5term AP: A020654 (>=0), A020655 (>0);
6term AP: A020656 (>=0), A005838 (>0);
7term AP: A020657 (>=0), A020658 (>0);
8term AP: A020659 (>=0), A020660 (>0);
9term AP: A020661 (>=0), A020662 (>0);
10term AP: A020663 (>=0), A020664 (>0).
Sequence in context: A045774 A045681 A001961 * A039116 A047201 A225496
Adjacent sequences: A020653 A020654 A020655 * A020657 A020658 A020659


KEYWORD

nonn


AUTHOR

David W. Wilson


EXTENSIONS

Edited by M. F. Hasler, Jan 03 2016
Further edited (with new offset) by N. J. A. Sloane, Jan 04 2016


STATUS

approved



