A003005 Size of the largest subset of the numbers [1..n] which doesn't contain a 6-term arithmetic progression.
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
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.
- 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.
- Terence Tao, Erdős problem database, see nos. 3, 139, 142.
- Samuel S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 (1972), 767-771.
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