A358935 - OEIS

%I #11 Dec 08 2022 01:51:40

%S 1,1,3,2,2,3,2,4,6,3,2,6,2,4,3,8,4,3,4,6,6,4,2,12,2,4,6,8,4,6,3,16,30,

%T 3,12,6,4,8,18,12,4,12,10,8,6,4,2,24,2,4,6,8,10,12,4,16,18,7,4,12,9,6,

%U 3,32,7,3,7,6,12,9,8,12,46,7,12,11,12,21,7

%N a(n) is the least k > 0 such that fusc(n) = fusc(n + k) or fusc(n) = fusc(n - k) (provided that n - k >= 0), where "fusc" is Stern's diatomic series (A002487).

%C Every positive integer appears infinitely many times in A002487, hence the sequence is well defined.

%H Rémy Sigrist, <a href="/A358935/b358935.txt">Table of n, a(n) for n = 1..8192</a>

%H Rémy Sigrist, <a href="/A358935/a358935.gp.txt">PARI program</a>

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

%F a(2^k) = 2^(k-1) for any k > 0.

%F a(n) = 2 iff n belongs to A097581 \ {2}.

%e The first terms, alongside fusc(n) and the direction where to find the same value, are:

%e   n   a(n)  fusc(n)  dir

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

%e    1     1        1  +

%e    2     1        1  -

%e    3     3        2  +

%e    4     2        1  -

%e    5     2        3  +

%e    6     3        2  -

%e    7     2        3  -

%e    8     4        1  -

%e    9     6        4  +

%e   10     3        3  -

%e   11     2        5  +

%e   12     6        2  -

%o (PARI) See Links section.

%Y Cf. A002487, A097581.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Dec 07 2022