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A358935 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).

%I A358935 #11 Dec 08 2022 01:51:40
%S A358935 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 A358935 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 A358935 3,32,7,3,7,6,12,9,8,12,46,7,12,11,12,21,7
%N A358935 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 A358935 Every positive integer appears infinitely many times in A002487, hence the sequence is well defined.
%H A358935 Rémy Sigrist, <a href="/A358935/b358935.txt">Table of n, a(n) for n = 1..8192</a>
%H A358935 Rémy Sigrist, <a href="/A358935/a358935.gp.txt">PARI program</a>
%H A358935 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A358935 a(2^k) = 2^(k-1) for any k > 0.
%F A358935 a(n) = 2 iff n belongs to A097581 \ {2}.
%e A358935 The first terms, alongside fusc(n) and the direction where to find the same value, are:
%e A358935   n   a(n)  fusc(n)  dir
%e A358935   --  ----  -------  ---
%e A358935    1     1        1  +
%e A358935    2     1        1  -
%e A358935    3     3        2  +
%e A358935    4     2        1  -
%e A358935    5     2        3  +
%e A358935    6     3        2  -
%e A358935    7     2        3  -
%e A358935    8     4        1  -
%e A358935    9     6        4  +
%e A358935   10     3        3  -
%e A358935   11     2        5  +
%e A358935   12     6        2  -
%o A358935 (PARI) See Links section.
%Y A358935 Cf. A002487, A097581.
%K A358935 nonn
%O A358935 1,3
%A A358935 _Rémy Sigrist_, Dec 07 2022