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Satisfies a(1)=1, a(A026835(n+1)) = a(n)+1, with a(m)=0 for all m not found in A026835, where A026835(n+2)=A026835(n+1)+a(n)+1.
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%I #4 Mar 30 2012 18:36:38

%S 1,2,0,3,0,0,1,4,0,0,0,1,1,2,0,5,0,0,0,0,1,1,1,2,0,2,0,3,0,0,1,6,0,0,

%T 0,0,0,1,1,1,1,2,0,2,0,2,0,3,0,0,1,3,0,0,1,4,0,0,0,1,1,2,0,7,0,0,0,0,

%U 0,0,1,1,1,1,1,2,0,2,0,2,0,2,0,3,0,0,1,3,0,0,1,3,0,0,1,4,0,0,0,1,1,2,0,4,0

%N Satisfies a(1)=1, a(A026835(n+1)) = a(n)+1, with a(m)=0 for all m not found in A026835, where A026835(n+2)=A026835(n+1)+a(n)+1.

%C Removing the leading '1' and all zeros results in the original sequence with every term incremented by 1.

%F Records occur at 2^n: a(2^n)=n+1.

%e Initialize all terms to zero. Set a(1)=1, go one term forward,

%e set a(2)=a(1)+1=2, go 2 terms forward,

%e set a(4)=a(2)+1=3, go 3 terms forward,

%e set a(7)=a(3)+1=1, go 1 term forward,

%e set a(8)=a(4)+1=4, go 4 terms forward,

%e set a(12)=a(5)+1=1, etc.

%e The indices 1,2,4,7,8,12,... form A085262.

%Y Cf. A085262.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 22 2003