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%I #5 Mar 30 2012 18:36:38
%S 1,2,1,3,1,1,2,1,4,1,1,1,2,1,2,1,3,1,1,2,1,5,1,1,1,1,2,1,2,1,2,1,3,1,
%T 1,2,1,3,1,1,2,1,4,1,1,1,2,1,2,1,3,1,1,2,1,6,1,1,1,1,1,2,1,2,1,2,1,2,
%U 1,3,1,1,2,1,3,1,1,2,1,3,1,1,2,1,4,1,1,1,2,1,2,1,3,1,1,2,1,4,1,1,1,2,1,2,1
%N Satisfies a(1)=1, a(A087158(n+1)) = a(n)+1, with a(m)=1 for all m not found in A087158, where A087158(n+2)=A087158(n+1)+a(n)+1.
%C Removing all the 1's results in the original sequence with every term incremented by 1.
%F Records are given by A055588(n): a(A055588(n))=n, where A055588(n)=Fibonacci(2n-2)+1 and Fibonacci(n)=A000045(n).
%e Initialize all terms to 1. 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=2, go 2 terms forward,
%e set a(9)=a(4)+1=4, go 4 terms forward,
%e set a(13)=a(5)+1=1, etc.
%e The indices 1,2,4,7,9,13,... form A087158.
%Y Cf. A087158, A085246.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 22 2003