%I #15 Mar 24 2021 09:52:08
%S 0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,
%T 1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,
%U 0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0
%N Parity of Greedy Catalan Base representation for n: a(n) = A014418(n) reduced modulo 2.
%C Also the rightmost digit in Catalan Base Representation A014418.
%C Characteristic function for A244223, numbers which have an "odd" representation in Greedy Catalan Base.
%H Antti Karttunen, <a href="/A244221/b244221.txt">Table of n, a(n) for n = 0..4862</a>
%F a(n) = A000035(A014418(n)) = A000035(A244161(n)).
%o (Scheme) (define (A244221 n) (A000035 (A244161 n)))
%o (Python)
%o from sympy import catalan
%o def a244160(n):
%o if n==0: return 0
%o i=1
%o while True:
%o if catalan(i)>n: break
%o else: i+=1
%o return i - 1
%o def a(n):
%o if n==0: return 0
%o x=a244160(n)
%o return 10**(x - 1) + a(n - catalan(x))
%o print([a(n)%2 for n in range(101)]) # _Indranil Ghosh_, Jun 08 2017
%Y Binary complement: A244220. Partial sums: A244225.
%Y A244226 gives the lengths of runs of identical terms. A244227 the lengths of runs of zeros.
%Y Cf. A244223, A014418, A244161, A000035.
%K nonn
%O 0
%A _Antti Karttunen_, Jun 23 2014