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A368798
Lexicographically earliest sequence of nonnegative integers such that the doubly-infinite symmetric sequence b defined by b(n) = b(-n) = a(n) for any n >= 0 has no three equidistant equal terms.
3
0, 1, 1, 2, 2, 3, 2, 1, 1, 3, 3, 4, 3, 2, 4, 4, 3, 2, 3, 1, 1, 3, 4, 4, 2, 1, 1, 2, 4, 5, 5, 6, 5, 5, 2, 3, 6, 6, 4, 5, 4, 5, 5, 3, 5, 6, 4, 4, 6, 2, 6, 7, 7, 8, 7, 1, 1, 5, 6, 2, 5, 1, 1, 2, 3, 5, 2, 5, 5, 3, 2, 7, 3, 1, 1, 6, 6, 7, 3, 1, 1, 6, 6, 3, 6, 4, 2
OFFSET
0,4
COMMENTS
This sequence is a variant of A006997.
By Van der Waerden's theorem, this sequence is unbounded.
LINKS
Rémy Sigrist, C++ program
EXAMPLE
For n = 5:
- the first 5 terms of the sequence are: 0, 1, 1, 2, 2,
- a(5) cannot equal 0 as we would have b(-5) = b(0) = b(5),
- a(5) cannot equal 1 as we would have b(-1) = b(2) = b(5),
- a(5) cannot equal 2 as we would have b(3) = b(4) = b(5),
- we chose a(5) = 3 as this does not induce tree equidistant equal terms.
PROG
(C++) See Links section.
CROSSREFS
Cf. A006997, A368795, A368808 (indices of records).
Sequence in context: A304041 A238509 A353932 * A253141 A100890 A262815
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Jan 06 2024
STATUS
approved