cp's OEIS Frontend

A257248 a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).

%I A257248 #12 Apr 19 2015 22:25:21
%S A257248 0,0,1,1,0,1,2,2,1,1,2,0,1,2,3,3,2,2,2,1,1,3,1,2,2,3,0,1,2,3,4,4,3,3,
%T A257248 3,2,2,3,2,2,2,4,1,1,3,2,3,1,3,4,2,2,1,2,3,3,4,0,1,2,3,4,5,5,4,4,4,3,
%U A257248 3,4,3,3,3,4,2,2,3,3,3,2,3,5,2,2,2,2,4,4,3,1,1,3,2,4,2,3,4,5,1,3,3,3,4,2,3,2,2,1,4,4,2,5,1,3,3,2,3,4,4,5,0,1,2,3,4,5,6,6
%N A257248 a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).
%C A257248 a(n) tells how many nonzero terms of A005187 are encountered when traversing toward the root of binary tree A233276, starting from the node containing n and before 1 is reached. This count includes both n (in case it is a term of A005187) but excludes the 1 and 0 at the root. See also comments in A257249, A256478 and A256991.
%H A257248 Antti Karttunen, <a href="/A257248/b257248.txt">Table of n, a(n) for n = 1..8192</a>
%F A257248 a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).
%F A257248 a(n) = A080791(A233275(n)). [Number of nonleading zeros in the binary representation of A233275(n).]
%F A257248 Other identities. For all n >= 1:
%F A257248 a(n) = A256478(n)-1 = A000120(A233277(n))-1.
%F A257248 a(n) = A070939(n) - A257249(n).
%o A257248 (Scheme, alternative definitions, the first one utilizing memoizing definec-macro)
%o A257248 (definec (A257248 n) (if (= 1 n) 0 (+ (A079559 n) (A257248 (if (zero? (A079559 n)) (A234017 n) (+ -1 (A213714 n)))))))
%o A257248 (define (A257248 n) (- (A256478 n) 1))
%Y A257248 One less than A256478.
%Y A257248 Cf. A000120, A000325, A005187, A070939, A079559, A080791, A213714, A234017, A233275, A233276, A233277, A255559, A257249, A256991.
%K A257248 nonn
%O A257248 1,7
%A A257248 _Antti Karttunen_, Apr 19 2015