A385993 - OEIS

%I #14 Aug 01 2025 11:05:49

%S 1,2,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,7,8,7,6,5,6,7,6,5,4,3,2,1,2,

%T 3,4,5,6,7,8,9,8,9,10,9,10,9,8,9,10,11,10,11,10,9,10,9,8,7,6,5,4,3,2,

%U 3,4,5,6,7,8,9,10,11,12,11,12,11,12,13,12,13

%N a(n) is the number of distinct values appearing an odd number of times among A002487(0), ..., A002487(n).

%H Rémy Sigrist, <a href="/A385993/b385993.txt">Table of n, a(n) for n = 0..8192</a>

%H Rémy Sigrist, <a href="/A385993/a385993.gp.txt">PARI program</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%F a(n) = - Sum_{k = 1, n} (-1)^A091948(k).

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

%F a(n) = 1 iff n = 0 or n belongs to A004171.

%e Sequence begins:

%e   n   a(n)  A091948(n)

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

%e    0     1           1

%e    1     2           1

%e    2     1           2

%e    3     2           1

%e    4     3           3

%e    5     4           1

%e    6     3           2

%e    7     2           2

%e    8     1           4

%e    9     2           1

%e   10     3           3

%e   11     4           1

%e   12     5           3

%o (PARI) \\ See Links section.

%Y Cf. A002487, A004171, A091948, A385991.

%K nonn

%O 0,2

%A _Rémy Sigrist_, Jul 14 2025