%I #10 Jan 12 2024 00:52:56
%S 1,10,10,100,10,100,100,1000,10,100,100,1000,100,1000,1000,10000,10,
%T 100,100,1000,100,1000,1000,10000,100,1000,1000,10000,1000,10000,
%U 10000,100000,10,100,100,1000,100,1000,1000,10000,100,1000,1000,10000,1000
%N Gould's sequence A001316 in binary.
%F Formulas due to Paul D. Hanna:
%F a(n) = 10^A000120(n).
%F a(n) = Product_{k=0..log_2(n)} 10^b(n,k) where b(n,k) = coefficient of 2^k in binary expansion of n.
%F a(n) = Sum_{k=0..n} (C(n,k) mod 2)*9^A000120(n-k).
%F G.f.: Product_{k>=0} 1 + 10*x^(2^k).
%o (PARI) a(n) = 10^hammingweight(n); \\ _Kevin Ryde_, Jan 11 2024
%Y Cf. A001316, A048883, A102376.
%K easy,base,nonn
%O 0,2
%A _Paul Barry_, Jan 05 2005