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%I #15 Apr 19 2015 22:25:29
%S 1,1,2,1,2,3,2,1,2,3,3,2,4,3,2,1,2,3,3,3,4,4,2,4,3,3,2,5,4,3,2,1,2,3,
%T 3,3,4,4,3,4,4,4,2,5,5,3,4,3,5,3,2,4,4,5,4,3,3,2,6,5,4,3,2,1,2,3,3,3,
%U 4,4,3,4,4,4,3,5,5,4,4,4,5,4,2,5,5,5,5,3,3,4,6,6,4,5,3,5,4,3,2,6,4,4,4,3,5,4,5,5,6,3,3,5,2,6,4,4,5,4,3,3,2,7,6,5,4,3,2,1,2
%N a(0) = 1, and for n >= 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).
%C Because A233275(n) = A003188(n) for n = 1 .. 9, a(n) = A005811(n) for n = 1 .. 9.
%H Antti Karttunen, <a href="/A257249/b257249.txt">Table of n, a(n) for n = 0..8191</a>
%F a(0) = 1, and for n >= 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).
%F Other identities. For all n >= 1:
%F a(n) = A070939(n) - A257248(n).
%F a(n) = A000120(A233275(n)). [Binary weight of A233275(n).]
%F a(n) = 1 + A256479(n) = 1 + A080791(A233277(n)).
%o (Scheme, alternative definitions, the first one utilizing memoizing definec-macro)
%o (definec (A257249 n) (if (zero? n) 1 (+ (- 1 (A079559 n)) (A257249 (if (zero? (A079559 n)) (A234017 n) (+ -1 (A213714 n)))))))
%o (define (A257249 n) (+ 1 (A256479 n)))
%Y One more than A256479.
%Y Cf. A000120, A003188, A005811, A055938, A070939, A079559, A080791, A213714, A234017, A233275, A233277, A233278, A257248, A256991.
%K nonn
%O 0,3
%A _Antti Karttunen_, Apr 19 2015
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