

A003004


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


7



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
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OFFSET

1,2


COMMENTS

These subsets have been called 5free 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
Fausto A. C. Cariboni, Sets that yield a(n) for n = 6..115, Apr 30 2018.
K. 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]
Z. Shao, F. Deng, M. Liang, X. Xu, On sets without kterm arithmetic progression, Journal of Computer and System Sciences 78 (2012) 610618.
S. S. Wagstaff, Jr., On kfree sequences of integers, Math. Comp., 26 (1972), 767771.


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


STATUS

approved



