A368795 - OEIS

%I #16 Jan 07 2024 16:33:39

%S 0,1,1,2,4,2,2,1,1,4,2,4,5,5,9,3,3,5,5,10,5,4,7,3,2,8,6,2,4,2,4,7,2,3,

%T 6,5,11,1,7,15,9,6,12,10,13,10,2,13,11,8,17,9,10,13,14,1,10,11,17,15,

%U 12,1,1,5,12,11,5,6,1,17,3,15,6,6,7,6,6,17,25

%N 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 terms in arithmetic progression.

%C This sequence is a variant of A229037 and A248625 with similar graphical features.

%H Rémy Sigrist, <a href="/A368795/b368795.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A368795/a368795.png">Scatterplot of the first 1000000 terms</a>

%H Rémy Sigrist, <a href="/A368795/a368795.txt">C++ program</a>

%H <a href="http://oeis.org/wiki/Index_to_OEIS:_Section_No#non_averaging">Index entries for non-averaging sequences</a>

%e For n = 4:

%e - the first 4 terms of the sequence are: 0, 1, 1, 2,

%e - a(4) cannot equal 0 due to the progression b(-4) = 0, b(0) = 0, b(4) = 0,

%e - a(4) cannot equal 1 due to the progression b(-2) = 1, b(1) = 1, b(4) = 1,

%e - a(4) cannot equal 2 due to the progression b(0) = 0, b(2) = 1, b(4) = 2,

%e - a(4) cannot equal 3 due to the progression b(2) = 1, b(3) = 2, b(4) = 3,

%e - we chose a(4) = 4 as this does not induce arithmetic progressions.

%o (C++) See Links section.

%Y Cf. A229037, A248625, A368797, A368798.

%K nonn,look

%O 0,4

%A _Rémy Sigrist_, Jan 06 2024