A020656 Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 6.

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

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 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.

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\(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

Crossrefs

Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):

3-term AP: A005836 (>=0), A003278 (>0);

4-term AP: A005839 (>=0), A005837 (>0);

5-term AP: A020654 (>=0), A020655 (>0);

6-term AP: A020656 (>=0), A005838 (>0);

7-term AP: A020657 (>=0), A020658 (>0);

8-term AP: A020659 (>=0), A020660 (>0);

9-term AP: A020661 (>=0), A020662 (>0);

10-term AP: A020663 (>=0), A020664 (>0).

Sequence in context: A045774 A045681 A001961 * A358849 A039116 A330002

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