

A020657


Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 7.


31



0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 84, 85
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OFFSET

1,3


COMMENTS

Also the set of numbers with no "6" in their base7 representation; see GerverRamsey, also comments in A020654.  Nathaniel Johnston, Jun 27 2011
Up to the offset, identical to A037470. There are lexicographically earlier, but nonmonotonic sequences which do not contain a 7term AP, e.g., starting with 0,0,0,0,0,0,1,0,...  M. F. Hasler, Oct 05 2014


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
J. L. Gerver and L. T. Ramsey, Sets of integers with no long arithmetic progressions generated by the greedy algorithm, Math. Comp., 33 (1979), 13531359.


MAPLE

seq(`if`(numboccur(6, convert(n, base, 7))=0, n, NULL), n=0..85); # Nathaniel Johnston, Jun 27 2011


PROG

(PARI) a(n)=vector(#n=digits(n1, 6), i, 7^(#ni))*n~ \\ M. F. Hasler, Oct 05 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):
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: A230872 A247832 A047368 * A037470 A187394 A057907
Adjacent sequences: A020654 A020655 A020656 * A020658 A020659 A020660


KEYWORD

nonn,easy


AUTHOR

David W. Wilson


EXTENSIONS

Name edited by M. F. Hasler, Oct 10 2014. Further edited by N. J. A. Sloane, Jan 04 2016


STATUS

approved



