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%I #38 Dec 09 2023 01:44:19
%S 0,1,1,2,1,3,4,2,1,3,7,9,10,5,6,3,13,15,16,8,4,2,1,3,7,22,11,14,7,9,
%T 13,28,14,7,18,9,20,10,5,12,6,3,8,4,2,1,3,7,13,22,11,23,30,15,20,10,5,
%U 28,14,7,37,40,20,10,5,12,6,3,8,4,2,1,3,7,13,53
%N a(1) = 0; a(2) = 1; thereafter a(n) = a(n-1)/2 if a(n-1) is even, otherwise a(n) = a(n-1) + a((n-1)-a(n-1)).
%H Gavin Lupo, <a href="/A352840/b352840.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=0.
%e a(2)=1.
%e 1 is odd, so a(3) = a(2) + a(2-a(2)) = a(2) + a(2-1) = a(2) + a(1) = 1 + 0 = 1.
%e 1 is odd, so a(4) = a(3) + a(3-a(3)) = a(3) + a(3-1) = a(3) + a(2) = 1 + 1 = 2.
%e 2 is even, so a(5) = a(4)/2 = 2/2 = 1.
%e Continuing, we get
%e n a(n)
%e - ----
%e 1 0
%e 2 1
%e 3 1 + a(1) 1 + 0 = 1
%e 4 1 + a(2) 1 + 1 = 2
%e 5 a(4) / 2 2 / 2 = 1
%e 6 1 + a(4) 1 + 2 = 3
%e 7 3 + a(3) 3 + 1 = 4
%e 8 a(7) / 2 4 / 2 = 2
%e 9 a(8) / 2 2 / 2 = 1
%e 10 1 + a(8) 1 + 2 = 3
%e 11 3 + a(7) 3 + 4 = 7
%e 12 7 + a(4) 7 + 2 = 9
%o (Python)
%o result = [0, 1]
%o iterations = 100
%o for i in range(1, iterations):
%o if result[i]%2 == 0:
%o result.append(result[i] // 2)
%o else:
%o result.append(result[i] + result[i - result[i]])
%o print(result, end='', sep=' ')
%o (MATLAB)
%o result = [0 1];
%o iterations = 100;
%o for i = 2:iterations
%o if mod(result(i), 2) == 0
%o result(i+1) = int32(result(i)/2);
%o else
%o result(i+1) = (result(i) + result(i - result(i)));
%o end
%o end
%Y Cf. A350129.
%K nonn,look,easy
%O 1,4
%A _Gavin Lupo_, Apr 05 2022
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