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.

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, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A368795 A368796 A368797 * A368799 A368800 A368801

Keyword

nonn,look

Author

Rémy Sigrist, Jan 06 2024

Status

approved