A003005 Size of the largest subset of the numbers [1..n] which doesn't contain a 6-term arithmetic progression. (Formerly M0459)

1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 22, 22, 23, 23, 23, 24, 25, 25, 26, 27, 28, 28, 29, 30, 31, 31, 31, 32, 33, 34, 34, 35, 36, 37, 38, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 46, 47, 47, 48, 48

Offset

1,2

Comments

These subsets have been called 6-free sequences.

References

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

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..147

Thomas Bloom, Problem 3, Problem 139, and Problem 142, Erdős Problems.

Fausto A. C. Cariboni, Sets that yield a(n) for n = 7..147, May 20 2018.

Erdős problems database contributors, Erdős problem database, see entry nos. 3, 139, 142.

Kevin O'Bryant, Sets of Natural Numbers with Proscribed Subsets, J. Int. Seq. 18 (2015) # 15.7.7.

Karl C. Rubin, On sequences of integers with no k terms in arithmetic progression, 1973. [Scanned copy, with correspondence]

Zehui Shao, Fei Deng, Meilian Liang, and Xiaodong Xu, On sets without k-term arithmetic progression, Journal of Computer and System Sciences 78 (2012) 610-618.

Samuel S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 (1972), 767-771.

Crossrefs

Cf. A003002, A003003, A003004, A065825.

Sequence in context: A247973 A352241 A195181 * A332204 A245321 A392332

Adjacent sequences: A003002 A003003 A003004 * A003006 A003007 A003008

Keyword

nonn

Author

N. J. A. Sloane

Status

approved