|
Search: id:A003002
|
|
|
| A003002 |
|
Size of the largest subset of the numbers [1...n] which doesn't contain a 3-term arithmetic progression.
(Formerly M0275)
|
|
+0
7
|
|
| 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
These subsets have been called 3-free sequences.
Actually, more terms of this sequence can be found directly from A065825, because A003002(n) (this sequence) = the integer k such that A065825(k) <= n < A065825(k+1). [From R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 18 2009]
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 (1972), 767-771.
|
|
CROSSREFS
|
Cf. A003003, A003004, A003005, A065825.
Sequence in context: A029130 A081611 A081228 this_sequence A087180 A029121 A161205
Adjacent sequences: A002999 A003000 A003001 this_sequence A003003 A003004 A003005
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
Extended from 53 terms to 80 terms, using a simple brute-force program with some pruning. R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 18 2009
|
|
|
Search completed in 0.002 seconds
|
