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%I #11 Jan 26 2015 08:23:44
%S 0,1,0,1,2,0,1,1,1,3,2,2,2,3,1,1,1,0,0,2,3,3,2,2,2,2,1,2,4,2,1,3,4,1,
%T 3,4,3,3,3,4,4,2,2,2,3,1,2,2,3,2,4,3,1,2,2,1,2,2,3,5,3,4,1,3,4,0,3,3,
%U 5,5,3,3,4,3,4,4,3,2,3,2,1,3,3,4,2,5,3,2,3,3,3,2,2,2,4,3,1,5,5,4,2,2,1,4,1,3,5,1,5,4,3,3,4,1,3,4,3,6,5,3,1,5,3,2,3,3,5,3
%N a(1) = 0, for n > 1: a(n) = a(A253889(n)) + floor((n modulo 3)/2).
%H Antti Karttunen, <a href="/A254045/b254045.txt">Table of n, a(n) for n = 1..8192</a>
%F a(1) = 0, for n > 1: a(n) = a(A253889(n)) + floor((n modulo 3)/2).
%F a(1) = 0, thereafter, if n = 3k+2, then a(3k+2) = 1 + a(k+1), otherwise a(n) = a(A253889(n)).
%F a(n) = A080791(A064216(n)). [Number of nonleading zeros in binary representation of terms of A064216.]
%F a(n) = A253894(n) - A254044(n).
%F Other identities and observations:
%F a(A007051(n)) = n for all n >= 0.
%F a(n) >= A253786(n) for all n >= 1.
%o (Scheme, three versions, first two using memoizing definec-macro)
%o (definec (A254045 n) (if (= 1 n) 0 (+ (A254045 (A253889 n)) (floor->exact (/ (modulo n 3) 2)))))
%o (definec (A254045 n) (cond ((= 1 n) 0) ((= 2 (modulo n 3)) (+ 1 (A254045 (/ (+ 1 n) 3)))) (else (A254045 (A253889 n)))))
%o (define (A254045 n) (A080791 (A064216 n)))
%Y Cf. A007051, A064216, A080791, A253786, A253889, A253894, A254044.
%K nonn
%O 1,5
%A _Antti Karttunen_, Jan 23 2015
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