A003004 Size of the largest subset of the numbers [1..n] which does not contain a 5-term arithmetic progression. (Formerly M0451)

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

Offset

1,2

Comments

These subsets have been called 5-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..115

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

Fausto A. C. Cariboni, Sets that yield a(n) for n = 6..115, Apr 30 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, A003005, A065825.

Sequence in context: A036701 A053756 A210436 * A120507 A303787 A090223

Adjacent sequences: A003001 A003002 A003003 * A003005 A003006 A003007

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(51) and beyond from Fausto A. C. Cariboni, Apr 30 2018

Status

approved