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A359866 a(n) is the number of k > 0 such that n-1-2*k >= 0 and a(n-1-2*k) >= a(n-1-k) >= a(n-1). 2
0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 3, 0, 4, 0, 3, 0, 3, 1, 0, 7, 0, 6, 0, 7, 0, 6, 0, 7, 1, 0, 9, 0, 10, 0, 8, 0, 10, 0, 9, 0, 10, 1, 0, 11, 0, 14, 0, 13, 0, 14, 0, 12, 0, 13, 1, 1, 3, 0, 17, 0, 17, 0, 18, 0, 17, 0, 18, 0, 17, 1, 2, 3, 0, 21, 0, 23, 0, 22, 0, 23, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,11
COMMENTS
This sequence is unbounded:
- by contradiction: suppose that a(n) < M for some fixed M,
- then, by Van der Waerden's theorem, we have an arithmetic progression of 2*M+1 indices where the sequence has the same value: say a(m) = a(m + k*r) for k = 0..2*M with m >= 0 and r > 0,
- this would imply that a(m + 2*M*r + 1) >= M, a contradiction.
This sequence has infinitely many 0's (if a(m) < a(n) for any m < n, then a(n+1) = 0).
LINKS
Rémy Sigrist, C program
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k's
-- ---- ------------
0 0 {}
1 0 {}
2 0 {}
3 1 {1}
4 0 {}
5 1 {2}
6 0 {}
7 1 {2}
8 1 {2}
9 0 {}
10 3 {1, 2, 3}
11 0 {}
12 4 {2, 3, 4, 5}
PROG
(C) See Links section.
CROSSREFS
Cf. A359867.
Sequence in context: A272474 A340426 A308717 * A297217 A218859 A363028
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Jan 16 2023
STATUS
approved

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Last modified July 18 06:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)