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 A233905 a(2n) = a(n), a(2n+1) = a(n) + n, with a(0)=0. 3
 0, 0, 0, 1, 0, 2, 1, 4, 0, 4, 2, 7, 1, 7, 4, 11, 0, 8, 4, 13, 2, 12, 7, 18, 1, 13, 7, 20, 4, 18, 11, 26, 0, 16, 8, 25, 4, 22, 13, 32, 2, 22, 12, 33, 7, 29, 18, 41, 1, 25, 13, 38, 7, 33, 20, 47, 4, 32, 18, 47, 11, 41, 26, 57, 0, 32, 16, 49, 8, 42, 25, 60, 4, 40, 22, 59, 13, 51, 32, 71, 2, 42, 22, 63, 12, 54 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS For every one bit in the binary representation of n, add the number represented by the substring left of it. LINKS Antti Karttunen, Table of n, a(n) for n = 0..8192 FORMULA a(n) = sum(k=0..floor(log(n)/log(2)), bittest(n,k) * floor(n/2^(k+1)) ) = sum(k=0..A000523(n), A030308(n,k+1) * floor(n/2^(k+1)) ), with bittest(n,k)=0 or 1 according to the k-th bit of n (the zeroth bit the least significant). a(n) = A011371(n) - A233931(n). EXAMPLE 27 is 11011 in binary, so we add 1, 110=6, and 1101=13, so a(27)=20. PROG (PARI) a(n)=if(n<1, 0, if(n%2, a(n\2)+n\2, a(n/2))) (PARI) a(n)=sum(k=0, floor(log(n)/log(2)), bittest(n, k)*floor(n/2^(k+1))) (Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library) (definec (A233905 n) (cond ((zero? n) n) ((even? n) (A233905 (/ n 2))) (else (+ (A233905 (/ (- n 1) 2)) (/ (- n 1) 2))))) ;; Antti Karttunen, Dec 21 2013 CROSSREFS Sequence in context: A286238 A286237 A059781 * A285284 A288183 A324055 Adjacent sequences:  A233902 A233903 A233904 * A233906 A233907 A233908 KEYWORD nonn AUTHOR Ralf Stephan, Dec 17 2013 STATUS approved

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Last modified April 13 12:29 EDT 2021. Contains 342936 sequences. (Running on oeis4.)