cp's OEIS Frontend

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.

%I A368798 #17 Jan 07 2024 16:28:56
%S A368798 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,
%T A368798 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,
%U A368798 5,3,2,7,3,1,1,6,6,7,3,1,1,6,6,3,6,4,2
%N 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.
%C A368798 This sequence is a variant of A006997.
%C A368798 By Van der Waerden's theorem, this sequence is unbounded.
%H A368798 Rémy Sigrist, <a href="/A368798/b368798.txt">Table of n, a(n) for n = 0..10000</a>
%H A368798 Rémy Sigrist, <a href="/A368798/a368798.txt">C++ program</a>
%e A368798 For n = 5:
%e A368798 - the first 5 terms of the sequence are: 0, 1, 1, 2, 2,
%e A368798 - a(5) cannot equal 0 as we would have b(-5) = b(0) = b(5),
%e A368798 - a(5) cannot equal 1 as we would have b(-1) = b(2) = b(5),
%e A368798 - a(5) cannot equal 2 as we would have b(3) = b(4) = b(5),
%e A368798 - we chose a(5) = 3 as this does not induce tree equidistant equal terms.
%o A368798 (C++) See Links section.
%Y A368798 Cf. A006997, A368795, A368808 (indices of records).
%K A368798 nonn,look
%O A368798 0,4
%A A368798 _Rémy Sigrist_, Jan 06 2024