A348080 - OEIS

%I #11 Oct 02 2021 04:28:39

%S 0,0,3,0,6,0,2,0,14,0,2,12,0,7,0,2,27,0,29,0,6,16,0,3,27,8,0,12,16,11,

%T 0,4,0,62,0,2,52,0,5,0,14,32,0,3,52,8,52,2,20,0,25,0,6,32,28,0,12,37,

%U 0,3,16,32,8,17,0,122,0,2,116,0,5,96,0,15,0,2,8

%N A variant of Van Eck's sequence: For n >= 1, if there exists an m < n such that a(m) = a(n), take the largest such m and set a(n+1) = n XOR m; otherwise a(n+1) = 0. Start with a(1)=0.

%C XOR denotes the bitwise XOR operator.

%C This sequence is unbounded, and contains infinitely many 0's.

%H Rémy Sigrist, <a href="/A348080/b348080.txt">Table of n, a(n) for n = 1..8192</a>

%H Rémy Sigrist, <a href="/A348080/a348080.png">Scatterplot of the first 2^20 terms</a>

%e The first terms, alongside m, are:

%e   n   a(n)  m

%e   --  ----  ---

%e    1     0  N/A

%e    2     0    1

%e    3     1  N/A

%e    4     0    2

%e    5     2  N/A

%e    6     0    4

%e    7     2    5

%e    8     2    7

%e    9     1    3

%e   10     6  N/A

%o (PARI) { p=vector(123); v=0; for (n=1, 77, print1(v", "); [p[1+v],v]=[n,if (p[1+v], bitxor(n, p[1+v]), 0)]) }

%Y Cf. A181391, A346516.

%K nonn,base,look

%O 1,3

%A _Rémy Sigrist_, Sep 27 2021