login
A003004
Size of the largest subset of the numbers [1..n] which does not contain a 5-term 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, 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
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, and X. Xu, On sets without k-term arithmetic progression, Journal of Computer and System Sciences 78 (2012) 610-618.
S. S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 (1972), 767-771.
CROSSREFS
KEYWORD
nonn
EXTENSIONS
a(51) and beyond from Fausto A. C. Cariboni, Apr 30 2018
STATUS
approved