%I
%S 0,0,1,0,2,2,5,0,0,4,21,4,10,10,5,0,42,0,85,8,8,42,341,8,0,20,1,20,
%T 170,10,1365,0,40,84,11,0,682,170,21,16,2730,16,5461,84,8,682,21845,
%U 16,0,0,85,40,10922,2,43,40,168,340,87381,20,43690,2730,17,0,16,80,349525,168,680,22,1398101,0,174762,1364,1,340,32,42,5592405,32,0,5460
%N a(1) = 0, and for n > 1, a(n) = 2*a(A332893(n)) + [n == 3 (mod 4)].
%C Base2 expansion of a(n) encodes the steps where numbers of the form 4k+3 are encountered when map x > A332893(x) is iterated down to 1, starting from x=n. See the binary tree illustrated in A332815.
%H Antti Karttunen, <a href="/A332896/b332896.txt">Table of n, a(n) for n = 1..16384</a>
%F a(1) = 0, and for n > 1, a(n) = 2*a(A332893(n)) + [n == 3 (mod 4)].
%F Other identities. For n >= 1:
%F a(2n) = 2*a(n).
%F a(A108546(n)) = A000975(n1).
%o (PARI) A332896(n) = if(1==n,n1,2*A332896(A332893(n)) + (3==(n%4)));
%Y Cf. A000975, A108546, A332815, A332893, A332895,
%Y Cf. also A292383.
%K nonn
%O 1,5
%A _Antti Karttunen_, Mar 04 2020
