A005839 Lexicographically earliest increasing nonnegative sequence that contains no 4-term arithmetic progression. (Formerly M0956)

0, 1, 2, 4, 5, 7, 8, 9, 14, 15, 16, 18, 25, 26, 28, 29, 30, 33, 36, 48, 49, 50, 52, 53, 55, 56, 57, 62, 64, 65, 66, 79, 86, 87, 88, 90, 93, 98, 101, 104, 105, 108, 109, 110, 121, 125, 135, 144, 148, 150, 151, 159, 162, 166, 168, 169, 170, 173, 175, 176, 182

Offset

1,3

Comments

a(n) = A005837(n) - 1. - Alois P. Heinz, Jan 31 2014

References

R. K. Guy, Unsolved Problems in Number Theory, E10.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

David W. Wilson, Table of n, a(n) for n = 1..10000 a(1..1001) from Alois P. Heinz

Mathematica

t = {0, 1, 2}; Do[s = Table[Append[i, n], {i, Subsets[t, {3}]}];
If[! MemberQ[Table[Differences[i, 2], {i, s}], {0, 0}], AppendTo[t, n]], {n, 3, 200}]; t (* T. D. Noe, Apr 17 2014 *)

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: A344406 A184164 A190852 * A254792 A062102 A092289

Adjacent sequences: A005836 A005837 A005838 * A005840 A005841 A005842

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jeffrey Shallit, Aug 15 1995.

Edited (with new offset, etc.) by N. J. A. Sloane, Jan 04 2016

Status

approved