%I #21 May 06 2021 09:44:27
%S 0,1,2,1,2,1,2,3,4,3,2,3,2,3,2,1,2,1,2,3,2,3,4,3,4,5,4,3,4,3,2,3,4,3,
%T 2,3,4,5,4,3,4,5,6,5,4,3,4,5,2,3,2,1,4,3,2,3,4,3,4,5,2,3,4,3,4,3,4,5,
%U 2,3,4,3,4,5,4,3,6,5,4,5,2,3,4,3,2,1,2
%N a(n) = A000120(A193231(n)); number of 1-bits in blue code for n.
%H Antti Karttunen, <a href="/A234022/b234022.txt">Table of n, a(n) for n = 0..8191</a>
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.19 "Invertible transforms on words", pp. 49--55. [Cf. especially pages 50 & 51].
%F a(n) = A000120(A193231(n)).
%F A000035(a(n)) = A000035(n) = (n mod 2) for all n. [Even terms occur only on even indices and odd terms only on odd indices, respectively]
%o (Scheme) (define (A234022 n) (A000120 (A193231 n)))
%o (Python)
%o def a065621(n): return n^(2*(n - (n&-n)))
%o def a048724(n): return n^(2*n)
%o l=[0, 1]
%o z=[0, 1]
%o for n in range(2, 101):
%o if n%2==0: l.append(a048724(l[n//2]))
%o else: l.append(a065621(1 + l[(n - 1)//2]))
%o z.append(bin(l[-1])[2:].count("1"))
%o print(z) # _Indranil Ghosh_, Jun 05 2017
%Y A234023 gives the positions where abs(a(n)-a(n+1)) > 1.
%Y Cf. A000120, A193231.
%K nonn
%O 0,3
%A _Antti Karttunen_, Dec 28 2013