A379850 - OEIS

%I #7 Jan 05 2025 10:16:10

%S 0,1,2,1,0,1,2,3,2,1,2,3,4,3,2,1,0,1,2,3,4,5,4,3,2,1,0,1,2,3,4,5,4,3,

%T 2,1,0,1,2,3,4,5,6,7,6,5,4,3,2,3,4,5,4,3,2,1,0,1,2,3,4,3,2,1,0,1,2,3,

%U 4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4,5,6

%N a(n) is the number of integers (positive or negative) v that appears in the set {A377091(k), k = 0..n} without -v appearing in it.

%C Does this sequence contain infinitely many zeros? If so, A377091 would contain every positive and negative integers.

%H Rémy Sigrist, <a href="/A379850/b379850.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A379850/a379850.gp.txt">PARI program</a>

%F |a(n+1) - a(n)| = 1.

%e The first terms, alongside A377091(n) and the corresponding v's, are:

%e   n   a(n)  A377091(n)  v's

%e   --  ----  ----------  ------------

%e    0     0           0  {}

%e    1     1           1  {1}

%e    2     2           2  {1, 2}

%e    3     1          -2  {1}

%e    4     0          -1  {}

%e    5     1           3  {3}

%e    6     2           4  {3, 4}

%e    7     3           5  {3, 4, 5}

%e    8     2          -4  {3, 5}

%e    9     1          -3  {5}

%e   10     2           6  {5, 6}

%e   11     3           7  {5, 6, 7}

%e   12     4           8  {5, 6, 7, 8}

%e   13     3          -8  {5, 6, 7}

%e   14     2          -7  {5, 6}

%e   15     1          -6  {5}

%e   16     0          -5  {}

%o (PARI) \\ See Links section.

%Y Cf. A377091.

%K nonn

%O 0,3

%A _Rémy Sigrist_, Jan 04 2025