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 A233904 a(2n) = a(n) - n, a(2n+1) = a(n) + n, with a(0)=0. 1
 0, 0, -1, 1, -3, 1, -2, 4, -7, 1, -4, 6, -8, 4, -3, 11, -15, 1, -8, 10, -14, 6, -5, 17, -20, 4, -9, 17, -17, 11, -4, 26, -31, 1, -16, 18, -26, 10, -9, 29, -34, 6, -15, 27, -27, 17, -6, 40, -44, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For every bit in the binary representation of n, if it is one then add the number represented by the substring left of it, and if it is zero subtract that. LINKS Antti Karttunen, Table of n, a(n) for n = 0..8192 Index entries for sequences related to binary expansion of n FORMULA a(n) = sum(k=0..floor(log(n)/log(2)), (2*bittest(n,k)-1) * floor(n/2^(k+1)) ) = sum(k=0..A000523(n), (2*A030308(n,k+1)-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) = A233905(n) - A233931(n). EXAMPLE 27 is 11011 in binary, so we add 1, subtract 11=3, add 110=6, and add 1101=13, so a(27)=17. PROG (PARI) a(n)=sum(k=0, floor(log(n)/log(2)), (2*bittest(n, k)-1)*floor(n/2^(k+1))) (PARI) a(n)=if(n<1, 0, if(n%2, a(n\2)+n\2, a(n/2)-n/2)) (Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library) (definec (A233904 n) (cond ((zero? n) n) ((even? n) (- (A233904 (/ n 2)) (/ n 2))) (else (+ (A233904 (/ (- n 1) 2)) (/ (- n 1) 2))))) ;; Antti Karttunen, Dec 21 2013 CROSSREFS Sequence in context: A250306 A120577 A104695 * A292576 A083275 A230892 Adjacent sequences: A233901 A233902 A233903 * A233905 A233906 A233907 KEYWORD sign AUTHOR Ralf Stephan, Dec 17 2013 STATUS approved

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Last modified July 22 22:40 EDT 2024. Contains 374544 sequences. (Running on oeis4.)