

A359866


a(n) is the number of k > 0 such that n12*k >= 0 and a(n12*k) >= a(n1k) >= a(n1).


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
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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



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



KEYWORD



AUTHOR



STATUS

approved



