|
%I M0459 #45 Oct 21 2023 01:07:43
%S 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,
%T 22,22,23,23,23,24,25,25,26,27,28,28,29,30,31,31,31,32,33,34,34,35,36,
%U 37
%N Size of the largest subset of the numbers [1..n] which doesn't contain a 6-term arithmetic progression.
%C These subsets have been called 6-free sequences.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Fausto A. C. Cariboni, <a href="/A003005/b003005.txt">Table of n, a(n) for n = 1..147</a>
%H Fausto A. C. Cariboni, <a href="/A003005/a003005.txt">Sets that yield a(n) for n = 7..147</a>, May 20 2018.
%H K. O'Bryant, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/OBryant/obr3.html">Sets of Natural Numbers with Proscribed Subsets</a>, J. Int. Seq. 18 (2015) # 15.7.7.
%H Karl C. Rubin, <a href="/A003002/a003002.pdf">On sequences of integers with no k terms in arithmetic progression</a>, 1973. [Scanned copy, with correspondence]
%H Z. Shao, F. Deng, M. Liang, X. Xu, <a href="http://dx.doi.org/10.1016/j.jcss.2011.09.003">On sets without k-term arithmetic progression</a>, Journal of Computer and System Sciences 78 (2012) 610-618.
%H Samuel S. Wagstaff, Jr., <a href="http://dx.doi.org/10.1090/S0025-5718-1972-0325500-5">On k-free sequences of integers</a>, Math. Comp., 26 (1972), 767-771.
%Y Cf. A003002, A003003, A003004, A065825.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
|
