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%I #6 Jan 17 2016 20:26:15
%S 0,1,0,2,1,0,1,3,2,1,0,2,1,1,2,4,3,2,1,0,3,2,1,2,1,1,3,2,2,2,3,5,4,3,
%T 2,1,0,4,3,2,1,3,2,1,2,1,1,4,3,2,3,2,2,3,2,2,2,4,3,3,3,3,4,6,5,4,3,2,
%U 1,0,5,4,3,2,1,4,3,2,1,3,2,1,2,1,1,5,4,3,2,4,3,2,3,2,2,4,3,2,3,2,2,3,2,2,2,5,4,3,4,3,3,4,3,3,3,4,3,3,3,3
%N a(n) = A080791(A267111(n)).
%H Antti Karttunen, <a href="/A267109/b267109.txt">Table of n, a(n) for n = 1..8192</a>
%F a(1) = 0; for n > 1, if A265332(n) = 1 [when n is one of the terms of A088359], a(n) = a(A004001(n)-1), otherwise 1 + a(n) = a(n-A004001(n)).
%F a(n) = A080791(A267111(n)).
%F Other identities. For all n >= 1:
%F a(n) = A070939(n) - A267108(n).
%o (Scheme, with memoization-macro definec)
%o (definec (A267109 n) (cond ((<= n 1) 0) ((= 1 (A265332 n)) (A267109 (- (A004001 n) 1))) (else (+ 1 (A267109 (- n (A004001 n)))))))
%Y Cf. A004001, A070939, A080791, A088359, A265332, A267108, A267110, A267111.
%K nonn
%O 1,4
%A _Antti Karttunen_, Jan 16 2016
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